Huh. Usually when Republicans talk about "election integrity" it's code for "making it harder to vote, so only fanatics and people who don't work for a living take the time to do it".
Simply adding a watermark sounds... fine, I guess. If it reassures people and gets them to join consensus reality, why not? The concern I'd have here is if they use it as a pretense to throw out perfectly legit ballots because "there was a crease through the watermark" or something. They'd have to defend it in court though.