Whatever you do, do NOT try to "manually" remove them with tweezers, a screwdriver, etc. When you break up majana/aiptasia it will spread like wildfire. Removing the rock will only help if you intend to throw it out.
One thing about those "button polyps"... if they are palythoa, they contain a pretty potent neurotoxin in their mucous. Google "palytoxin" and you'll get the info you need. Short story is wear latex gloves when handling them, and if you're doing something that may cause them to squirt stuff (like cutting them) wear eye protection.