It might depend on your jurisdiction, but LLM output is usually not copyrightable because it is not made by a human. There might be a few exceptions, if you guided the LLM in very specific and particular ways. But in general, the output of an LLM is public domain the moment it was produced.

Can you never tell anybody and just slap a license on it? Sure.

The issue here is not the license, but that you violate their ToS (if that is valid and enforceable is a different question of course). But if you publish the LLM output on github, and someone else takes it to train their LLM, and you did not actively encourage or help them, it's fine.