Inserting an undetectable 1-bit watermark into a multi megapixel image is not particularly difficult.

If you assume competence from Google, they probably have two different watermarks. A sloppy one they offer an online oracle for and one they keep in reserve for themselves (and law enforcement requests).

Also given that it's Google we are dealing with here, they probably save every single image generated (or at least its neural hash) and tie it to your account in their database.