Not to mention the copyrightability of AI output isn't legally well tested, and chances are it'll fall in the direction of being copyrighted by the user (i.e. the person clicking in the UI to make a character, which is where creative input happens), not by the AI creator (who has no creative input into the process; they merely made a tool, like any other piece of software - same reason documents printed from Microsoft Word aren't copyrighted by Microsoft).
I'm not entirely sure how much legal weight a ToS on the website would have on what the users do with the output. As I understand it, you could e.g. forbid explicitly using the service/generator for commercial purposes (e.g. during game development), but if someone generates a cool character playing around with no particular commercial objective and then decides post facto to build a media megafranchise out of that character, absent any copyright claim over the image, I don't think there's anything stopping them. They wouldn't even need to trace over it, though if they want new artwork in different poses, they couldn't keep using the AI for that with explicit commercial intent; they'd have to get humans to re-draw it.
Alternatively, a pessimistic view of the interaction between copyright and AI would be that the model is a derivative work of all the training input, and its output also is, and then good luck building a non copyright infringing AI.
IANAL and all that, but it would definitely be legally risky to assume that as the provider of an AI generator you have any control over what users do with the output.