Peppermint shrimp are also supposed to eat bristleworms too, but mine never did. They are also supposed to eat baby zoanthids too, and I was worried about it because I found this out after I bought two, but mine never did.
I think the difference is between aquacultured peppermints and wild-caught ones. The aquacultured peppermints probably never see aptaisia, so they never learn that it is "food", unless their instincts kick in.
Anyone around here know how what the percentage is between wild-caught and aquacultured pepps for sale at the LFS?
I put some lemon juice on the rock with my two aptaisia (even before I got the peppermint shrimp) and that killed it dead, never to return. I poured some salt on it too for good measure.
I read that you can get a needle from the pharmacist and inject the lemon juice into the aiptasia, and kill it that way. Any lemon juice that gets away will be quickly neutralised by your tank's buffering capacity and not harm even critters right next to it, which was shown by pictures of people who did that to aiptasia that was growing on next to their expensive coral.