Thing is they are fairly toothless given all they really have is their branding. The most they can do is either:
1) Withdraw heritage status from a location
2) Write a strongly worded letter to Government/Local Council/Developer/Other threatening to withdraw heritage status from a location
Since most places that have heritage status only use it for tourism promotions and this island only has 13 tourist trips a year, threatening to destroy the tourism is pointless...