In the US, at least, the works generated by "AI" are not copyrightable. So for my layman's understanding, they may claim ownership, but it means nothing wrt copyright.
(though patents, trademarks are another story that I am unfamiliar with)
There's a difference between an AI acting on it's own, vs a person using AI as a tool. And apparently the difference is fuzzy instead of having a clear line somewhere.
I wonder if any appropriate-specialty lawyers have written publicly about those AI agents that can supposedly turn a bug report or enhancement request into a PR...
But along the same argument you may claim ownership, but it means nothing wrt copyright.
So you cannot stop them from using the code AI generated for you, based on copyright claims.