If you google "Death Island" the first 16 hits refer to Ko Tau.
Nothing can be done to protect Thailand's tourism reputation in this regard. (Or any regard for that fact.)
Ok so it's a "myth" that it's a dangerous island controlled by resident mafia types, but the reputation itself is no myth. It's a fact!
After unsuccessfully gooling to find a humorous meme to post, I find that there are heaps of places that are dark tourist destinations and morbid tourist attractions.
I'm not advocating TAT should come out with a "Ko Tau, Hub of Mysterious Deaths" promo campaign. It seems like every knows already.
And there seems to be enough stupid <deleted> who want to go diving, boozing and 420ing in an edgy location.
So maybe it's time to take the traditional Thai approach and do nothing