I presume anything ChatGPT generates belongs to the user who asked for the code to be generated. Is there any clause in the EULA that says this is the case? Or is code generated by ChatGPT automatically BSD-licensed? Or can ChatGPT claim ownership or joint-ownership of code generated using their tools?
Another question is the code it was trained on. Presumably all of it was open source. BSD-licensed code typically requires attribution. GPL code requires anything copied to remain GPL. If the GPT is reproducing small stanzas of code from memory it probably doesn't matter. If GPT reproduces larger blocks of code from stuff that it was trained on, there is a possibility of failing to comply with copyright.