How to check if uploaded image has a watermark?

No. At least not easily. It's just an image. It's not like there are layers to the image and all it has to do is check for a "watermark" layer. If I had a picture of myself with a road sign in the background of the image, how would it be able to tell whether the text on the road sign was a watermark, or part of the actual image? There are services that can help with detection, but they aren't free and aren't 100% accurate. It's harder than facial recognition.

Hi @Cronix I understand. I just don't want users to upload licensed images. Is there a way to check for a license? I read something about meta?

Yes, you can read exif metadata ( http://php.net/manual/en/function.exif-read-data.php )

It might help a bit, but isn't reliable since it can be altered/deleted and some newer phones (and some services) delete it to protect privacy (like gps coordinates).

I think there's no solution with this. Since it is on front end part, though there is something around the internet you can use, you cannot check if it is 100% accurate. @Cronix is correct.