Redsea is correct..that looks like Aiptasia

. There is a substance out called Aiptasia-X which could/should be available at your
LFS. Another method is Kalkwasser (
Kalk). 2 tablespoons water to one tablespoon
Kalk powder..mix well into a thin paste. Turn off anything that makes the water move, filters, powerheads etc. Suck up the mixture into the syringe and then carefully coat the aiptasia and its hole with the mixture. This is kind of an important point and shoot operation as concentrated
Kalk may also kill other corals and such if the mixture lands heavily enough. You are going to see what looks like a white powder. The aiptasia wil immediately retract as soon as it senses anything nearby but coating the hole will be enough to kill it. Leave your filters and such off for fiftenn minutes and then turn back on. What
Kalk blows around the tank won't hurt anything..it isn't concentrated enough at that point.
If you get the concentrated
Kalk on something else, just blow it off gently with something..like you would when clearing dust and such off of liverock...it doesn't kill immediately.
As for Peppermint shrimp..it is a 50/50 shot. From what I understand, there are different versions of Aiptasia in the Atlantic and Pacific. If the Peppermint shrimp are from one area and the Aiptasia you have are from another, the Pepps won't recognize it as a food source. If you have the tank room it can't hurt to try but Pepps are not always successful. If you know for sure wher ethe liverock came from, the Atlantic version of the Aiptasia actually doesn't reproduce like the Pacific version. The
LFS I get my liverock from aquacultures it in Florida. I have one Aiptasia that arrived with it and even after 6 months, I still only have that one. I have let it "live" since it is cooperating and not taking over the tank.
I have been on the hunt before though and had to eradicate 4 on other rock before putting it in the main display. That rock was a transfer from a friend's tank.