[omnimus]

This has been problematic forever long even before any LLMs. Techniques like photobashing that use copyrighted images modify them for it to be new work. Or even older cases like work of Andy Warhol.

Where this is more extreme here is that there is no human labor involved there is no invention. On the other hand LLMs make this extra tricky because in one way output they create is objectively unique but subjectively/culturally it's not.

To answer your question if you take AI generated image and change it enough for it to stand as it's own unique thing you could for sure claim it as your work and it would be eligible for copyright.