If the tissue dies, it will just decompose and the healthy tissue will heal over. The tissue does not separate from the anemone by itself unless it is dead. Some may want to use a razor blad to cut the damaged portion out, but in this case, I feel that you will just leave it the way it is, and put it near mild flow area so that the current is strong enough to keep it well oxygenated and carry away the dead tissue (once it come loose), but weak enought that it won't cause physical stress or additional tear/laceration on the anemone (I know this can be a bit of catch-22, but do your best. hint: milder current is better since if you feel the current is not strong enough, you can use your hand to gently fan the decompose away). It may sounds like a contradiction, but the rule of thumb in most injury is to leave it as much as you can. The more you bother it, the more likely it will heal slower. Good luck.
) so you can keep your filter running.
