alt Hacker NewsYour question has nothing to do with the GPL. If your concern is that the code may count as derivative work of existing code then you also can't use that code in a proprietary way, under any license. But that probably only applies if the LLM regurgitated a substantial amount of copyrighted code into your codebase.
Fair; that was an example instance. People interested in “Free software” rather than “open source” seem to often favor the GPL, though other licensing options also count as “free software”.
But in any case, the question really refers to, can the LLM-generated software be copyrighted? If not, it can’t be put under any particular license.