You have no clue how fast these things will spread if there are already several. Newcomers often think they look nice so they ignore them, but if you leave them they overcome EVERYTHING. I've seen tanks that are nothing but rock covered in massive colonies of aptasia before. If you want actual anemones eliminate these and get a non-pest species.
The way I got rid of mine was to inject kent marine liquid calcium into them with a very fine syringe, like a diabetic needle (and you have to do it quickly or else the anemone will pull back and you won't get it in there).
As far as peppermint shrimp, they won't eat much of it. And many of them ignore it altogether if they have other food sources. There are a few crabs that will pick at them, but again, unlikely they'll actually eliminate them from tank.
The filefish mentioned is a really good eliminator, but then you have to figure out what to do with the filefish after he's done because long term they'll likely pick at or destroy any corals you have.