Of course it does this. The training data is full of examples that associate e.g. "New Yorker-style cartoon" with Loper's signature in the corner, because Loper's signature is in the corner of a lot of them. There's nothing to make it treat the signature as anything special by default; that would have to be trained in explicitly.

One would hope that the person prompting ChatGPT would notice this sort of thing and do something about it before sharing it publicly, out of a genuine desire not to cause confusion etc. But I guess that's way more personal responsibility than we can expect average people to take on nowadays.