Button polyps typically refers to palythoa, which secrete a toxin that can significantly harm your health. With palythoa you may want to just remove the rock from your system and try to trade it into you lfs for live rock. Star polyps grow in a mat, and typically with enough time, patience, and elbow grease you can peel it off. You do not want to scrub as that will cause it to spread to other rocks. You can also place a kalk slurry on top that will irritate it. If done enough times it will cause them to melt away.
It might be better if you get a clear picture of exactly which corals you are indicating. Also if you can turn the whites on, that would make it easier.
Those are mushroom coral and you could sell them to make a few bucks or trade them in at lfs. If your looking to get rid of some and you would ship maybe we could work something out. PM me if your interested.