I’ve read that  when Hallmark bought the Filmation library, they transferred the negatives to television prints and then destroyed the negatives.

It's likely that this isn't public information, but did this policy apply to specific Filmation shows that contain characters not owned by them? I’m specifically thinking of The Tom and Jerry Comedy Show and The New Adventures of Mighty Mouse and Heckle and Jeckle in this case, but there are several other cases, like with Star Trek: The Animated Series and The New Adventures of Gilligan.

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Hallmark only scanned and destroyed the film material they had direct ownership of. Most or all of the Filmation material that went out to other companies (MGM, Viacom, Paramount, etc.) survived because they became the sole owner of the original material. In fact, on the Warner Archive Podcast episode on their New Adventures of Gilligan set they stated they went back to the original negatives for restoration.

This is where it's advantageous that Filmation did so many adaptations of existing properties instead of creating original characters. The Filmation library is really scattered to the four winds because of this. Here's what I know:

Filmation's adaptations of DC Comics superheroes (including the Shazam segments of the live action The Shazam/Isis Power Hour) belong to WB.
The "Daffy Duck and Porky Pig Meet the Groovie Goolies" Saturday Superstar Movie belongs to WB.
The New Adventures of Gilligan and Gilligan's Planet belong to WB.
The Tom and Jerry Comedy Show belongs to WB.
The "The Brady Kids on Mysterious Island" Saturday Superstar Movie belongs to Paramount.
The Brady Kids belongs to Paramount. (But I don't know if Paramount had to pay royalties to WB to include the episodes with Superman and Wonder Woman when The Brady Kids was released on DVD.)
Star Trek: The Animated Series belongs to Paramount.
The Mighty Mouse and Heckle & Jeckle segments of The New Adventures of Mighty Mouse and Heckle & Jeckle belong to Paramount. (But not the Quacula and "The Great Space Chase" segments.)
Filmation's Journey to the Center of the Earth animated series belongs to 20th Century Fox.
Filmation's Fantastic Voyage animated series belongs to 20th Century Fox (and has been released on DVD in the UK).
The "Lassie and the Spirit of Thunder Mountain" Saturday Superstar Movie belongs to Classic Media.
Lassie's Rescue Rangers belongs to Classic Mediia.
Filmation's Lone Ranger animated series belongs to Classic Media.
Filmation's Flash Gordon animated series belongs to Hearst/King Features Syndicate.
And I assume that My Favorite Martians belongs to MGM but I'm not positive.

Here's what I'm not sue about:

I don't know if Filmation's adaptations of Archie Comics characters belong to the current owners of the Filmation library or if they belong to Archie Comics. (Though I assume that WB owns Josie and the Pussycats and Josie and the Pussycats in Outer Space, not Archie Comics.)
I don't know if He-Man and the Masters of the Universe and She-Ra: Princess of Power belong to the current owners of the Filmation library or if they belong to Mattel.
I don't know if Fat Albert and the Cosby Kids and the Fat Albert holiday specials belong to the current owners of the Filmation library or if they belong to Bill Cosby. (Though I'm inclined to believe the former because I don't think Bill Cosby owns any of the other TV series he created and starred in.)
I don't know if Will the Real Jerry Lewis Please Sit Down belongs to the current owners of the Filmation library or if it belongs to the estate of Jerry Lewis.
I don't know if Filmation's Hardy Boys animated series belongs to the current owners of the Filmation library or if it belongs to someone else because I don't know if the Hardy Boys are considered a licensed property.
I don't know if Filmation's adaptations of Tarzan belong to the current owners of the Filmation library or if they belong to someone else because I don't know if the character of Tarzan is in the public domain.
Likewise I don't know if Filmation's adaptation of Zorro belongs to the current owners of the Filmation library or if it belongs to someone elsebecause I don't know if the character of Zorro is in the public domain. (Though I'm inclined to believe the former since Disney released its Zorro TV series from the 1950's as Disney Treasures. And I don't even want to talk about Zorro: The Gay Blade, which I actually saw with my dad when it was in theaters.)
I'm wondering if Sport Billy was an adaptation of an existing property because it was included in the first batch of cartoons that ran on the USA Network Cartoon Express in 1983, which was otherwise all Hanna-Barbera cartoons.
And who knows who owns Archie's TV Funnies and Fabulous Funnies because I don't know if the comic strip characters in these shows all belong to the same syndicate.

And there's always the possibility that the current owners of the Filmation library own these TV series but had to pay royalties to the owners of the characters to be able to release them on DVD, like WB is having to pay royalties to Hearst/King Features Syndicate to be able to release the theatrical Popeye cartoons on DVD and Blu-ray. (Event though AAP had to pay Hearst/King Features Syndicate a million dollars when they bought the theatrical Popeye cartoons in the 1950's.)

What does that leave that definitely belongs to the current owners of the Filmation library? Going from a combination of memory and Wikipedi:

Rod Rocket
The Groovie Goolies segments of Sabrina and the Groovie Goolies. (But maybe not the Sabrina segments of this series and Sabrina, Superwitch that the Groovie Goolies appeared in.)
Aesop's Fables
Mission: Magic!
The Secret Lives of Waldo Kitty (Even though Waldo Kitty's alter egos are based on existing characters like Batman and Captain Kirk.)
The animated segments ("M-U-S-H", "Fraidy Cat" and "Wacky and Packy") of Uncle Croc's Block, though some of these segments may be in the public domain. (The live action segments may not survive.)
The Young Sentinels (aka The Space Sentinels)
The "Web Woman", "Freedom Force", "Manta and Moray" and "Superstretch and Microwoman" segments of Tarzan and the Super 7. (I have a "homemade" DVD set with just these segments with the title The Super 7, so they may have been syndicated.)
Blackstar
The Quacula and "The Great Space Chase" segments of The New Adventures of Mighty Mouse and Heckle & Jeckle
BraveStarr
The Ghost Busters (live action and animated)
The Isis segments of the live action The Shazam/Isis Power Hour
The live action series Ark II
The live action series Space Academy
The live action series Jason of Star Command
A Snow White Christmas (with Snow White's daughter and the "Seven Friendly Giants")
Filmation's adaptations of Treasure Island and Oliver Twist
Filmation's animated features (not counting the ones that were cobbled together from episodes of TV series): Journey Back To Oz (which I actually saw when it was in theaters), Pinocchio and the Emperor of the Night, Happily Ever After and BraveStarr: The Movie

And I'm sure there's other stuff that I've left out.

What's sad is that Filmation actually sprung for Technicolor. So at least some Technicolor negatives got destroyed.

P.S. Phew!

a lot of this info is outdated, created from an old story with holes in it. there is no evidence hallmark actually destroyed the filmation masters, but there is no evidence they didn't, either. they made their masters from a variety of sources, including the camera negatives (e.g. The Archie Show) and 35mm (not 16mm) prints (e.g. My Favorite Martians). however, hallmark absolutely did not destroy older analog tape masters or even their own ntsc masters, contrary to the popular belief that they only made pal masters. he-man/she-ra superfan James Eatock had a brief stint with classic media in 2016 and found analog tape masters for he-man at the UK warehouse where filmation material lives. he told me their database was very messy and almost nothing was in the right place. a he-man soundtrack full of audio cues from original masters was released a few years back. whether these came from classic media or shuki levy himself is beyond me. NBCUniversal currently distributes A Snow White Christmas with an old 80s master instead of Hallmark's.

Shazam! (1981) rights were retained by Filmation, despite the Warner Bros./DC connection.
Daffy Duck and Porky Pig Meets the Groovie Goolies (1972) is owned by Filmation, and even survived into Entertainment Rights' catalog as a split two-parter for the series for years. A German dub aired on television around 2013.
Lassie and Lone Ranger rights were retained by Filmation. As Classic Media now owns the library, the point is a little moot.
My Favorite Martians belongs to Filmation. Jack Chertok's company handled licensing. A DVD/streaming release was in the works according to Andy Mangels, but the owner of said company passed away.
Jerry Lewis seemingly belongs to Paramount through their ownership of Worldvision/ABC Films, who syndicated the series. There is no evidence pointing to Filmation owning the negatives. (ABC Films syndicated just about every show they aired that season. For example, Smokey Bear, which is owned by Classic Media.)
Quacula and Great Space Chase belong to Paramount.
Hardy Boys likely belongs to 20th Century Fox.
Aesop's Fables, Tarzan, Treasure Island, and Oliver Twist are handled by Warner Bros. (Aesop through ownership of Lorimar)
Warner Bros. holds non-US rights to Journey Back to Oz. US rights are held by Filmation. (Classic Media)
Archie, Sabrina, He-Man, She-Ra, Fat Albert, Fabulous Funnies, TV Funnies, and Zorro are in the Filmation library.
Sport Billy was handled by Sport-Billy Produktions and Telemundi AG. The current state of both companies is unknown.
The ownership of Rod Rocket is unknown. Alice Communications allegedly syndicated it in the 80s, as per Lou Scheimer's autobio. (if i recall correctly)

the color was processed at the Technicolor labs. likely eastmancolor negs. i imagine technicolor negatives would have been cost prohibitive for television and likely entirely out of the question by the time filmation was making things.

At least I got some of it right. So all of my hard work wasn't completely for nothing.

a lot of this info is outdated, created from an old story with holes in it. there is no evidence hallmark actually destroyed the filmation masters, but there is no evidence they didn't, either. they made their masters from a variety of sources, including the camera negatives (e.g. The Archie Show) and 35mm (not 16mm) prints (e.g. My Favorite Martians). however, hallmark absolutely did not destroy older analog tape masters or even their own ntsc masters, contrary to the popular belief that they only made pal masters. he-man/she-ra superfan James Eatock had a brief stint with classic media in 2016 and found analog tape masters for he-man at the UK warehouse where filmation material lives. he told me their database was very messy and almost nothing was in the right place.

Do you know if the live action segments from Uncle Croc's Block survive? It was cut up when the animated segments were packaged with the syndicated The Groovie Goolies and Friends.

NBCUniversal currently distributes A Snow White White Christmas with an old 80's master instead of Hallmark's.

I have a UK DVD of A Snow White Christmas. But all of my DVD's are in storage so I can't check the quality.

Shazam! (1981) rights were retained by Filmation, despite the Warner Bros./DC connection.

The Isis segments from The Shazam/Isis Power Hour were released separately on DVD. That's why I assumed that WB had the rights to Filmation's adaptations of Shazam/Captain Marvel.

Lassie and Lone Ranger rights were retained by Filmation. As Classic Media now owns the library, the point is a little moot.

I knew that Classic Media owned the live action Lassie and Lone ranger TV series. So I assumed that they owned the Filmation adaptations as well..

Hardy Boys likely belongs to 20th Century Fox.

The Hardy Boys serial "The Treasure of Applegate" that aired as part of the original Mickey Mouse Club was released as a Disney Treasure, so I assume that Disney owns it. And the Hardy Boys/Nancy Drew TV series from the late 1970's (which I watched during its original run) was released on DVD by Universal. That's why I wondered whether or not the Hardy Boys are a licensed property.

(Also, since it's kind of a related property, the Warner Brothers Nancy Drew movies from the late 1930's/early 1940's were released on DVD by WB and occasionally air on Turner Classic Movies. So I assume that they belong to WB. And the Nancy Drew TV series that's currently airing on the CW is being released on DVD by Paramount.)

the color was processed at the Technicolor labs. likely eastmancolor negs. i imagine technicolor negatives would have been cost prohibitive for television and likely entirely out of the question by the time filmation was making things.

I saw "Color by Technicolor" in the end credits while watching Filmation TV series on DVD. That's why I assumed that they were filmed with Technicolor negatives.

the status of uncle croc's block is completely unknown to me. i do know that viacom syndicated it internationally and it aired in australia for a few years (late 70s/early 80s). b&w prints do exist out there

My question is, did Filmation still have their unsold pilots in their masters when Hallmark destroyed what they owned? I know they were missing a few Archie negatives that I believe have turned up, so I wonder what happened to some of these pilots. Tommy uploaded an intro from one  today that made me think of this, as I believe another, earlier pilot from the 60s surfaced in 16mm as well

filmation had masters made for dick digit and king arthur, they surfaced on a UK blackstar vhs tape in the 80s. king arthur was also part of the groovie goolies and friends syndication package to help fill an uneven gap left by the uncle croc cartoons.