Earlier quoted context omitted.
I don't think it will be easy to just remove it. It's built into the image and thus won't be the same every time. Plus, any service good at reverse-image search (like Google) can basically apply that to determine whether they generated it. There will always be a way to defeat anything, but I don't see why this won't work for like 90% of cases.
It's an image. There's simply no way to add a watermark to an image that's both imperceptible to the user and non-trivial to remove. You'd have to pick one of those options.
It may be easier if you have an oracle on your end to say "yes, this image has/does not have the watermark," which could be the case for some proposed implementations of an AI watermark. (Often the use-case for digital watermarks assumes that the watermarker keeps the evaluation tool secret - this lets them find, e.g, people who leak early screenings of movies.)