You don't have any recourse, at least not under American law. This a textbook third-party doctrine case: American law and precedent is unambiguous that once you voluntarily give your data to a third party-- e.g. when you sent it to OpenAI-- it's not yours anymore and you have no reasonable expectation of privacy about it. Probably people are going to respond to this with a bunch of exceptions, but those exceptions all have to be enumerated and granted specifically with new laws; they don't exist by default, and don't exist for OpenAI.
Like it or not, the judge's ruling sits comfortably within the framework of US law as it exists at present: since there's no reasonable expectation of privacy for chat logs sent to OpenAI, there's nothing to weigh against the competing interest of the active NYT case.
Like it or not, the judge's ruling sits comfortably within the framework of US law as it exists at present: since there's no reasonable expectation of privacy for chat logs sent to OpenAI, there's nothing to weigh against the competing interest of the active NYT case.