i wish i could go into some of the stuff Nickelodeon has had me change but i won't for the sake of professionalism, but i'm not working on TMNT at the moment and probably not for the foreseeable future, so i'll say more than i would otherwise.
as far as i know the only main mandate from up high is that the Turtles can't kill. obviously i'm just an artist and a sporadic one at that, i don't know what goes on with the powers that be, but i was involved in the script process on the stories i've drawn and privy to the changes that were requested and made, but the changes are mostly relegated to individual cases. they were even cool with me suggesting my own ideas, like April's haircut in Northampton, or Pepperoni in Turtles in Time. same with the art, i've never been given any mandates on what i must do or can't do. there's no mandate that the Turtles look like the Nickelodeon cartoon Turtles, in fact Mateus has stated elsewhere that there was some concern that they SHOULDN'T look like the cartoon Turtles (also look at Andy Kuhn, Charles Wilson III, etc.).
from what i can tell the Nickelodeon higher-ups aren't involved, we deal with a couple freelance and in-house editors whose requests are vary on a case by case basis, and sometimes they change from day to day, like one day they'll remark on an aspect of character design that they don't like, but then it's fine in the next instance of the same thing. it all depends on the individual scene or drawing. the editors' personal preferences are probably the largest factor. they're people, too, they have their own preferences and dislikes like anyone does.
i've had a few battles with the Nick editors, i have no problem fighting with them and being a diva to get my way, and the little things that they fuss about can get on my nerves, but overall they're extremely lenient. the Alopex issue and Turtles in Time #1 in particular, those were a breeze, they didn't have me change anything art-wise. it was all me. aside from one huge fight, Northampton was also a great experience, they let me do anything i wanted. the worst experience i've had was when i pitched to write the April O'Neil micro issue, it was an awful, soul-crushing experience. the story was eventually rejected at the last minute.
i think the Nick editors have also gotten much more casual and lenient as the comic series has progressed, too, as it's settled into what it is and everyone knows more what it's about and it's less amorphous than it was in the early days. there's more leeway now. it seems like they're also much harder on writers than they are on the artists.
i see a lot of people speculating about what goes on behind the scenes with licensed comics, like the parent companies handing down lists of corporate mandates and restrictive marketing campaigns and all that, but most of the time that's not the case. with Nickelodeon and Hasbro, it's all really lenient and casual. all the TMNT stuff has to go through the approval process, yeah, but for the most part things end up how the artists want to draw them. you guys wouldn't believe how hands-off Hasbro is, i've seen people theorizing about all the behind-the-scenes corporate maneuvering on the Jem & the Holograms i'm working on now, but the art is seriously all me. they basically turned me loose to do whatever the hell i want. Nickelodeon is more restrictive, but they largely turned me loose, too.
anyway, i felt like i should step in here and give my two cents and tell you guys some of the experiences i've had personally. and of course i can't speak for the other TMNT creators, these experiences are my own.