Aiptasia typically aren't particularly harmful, but once they get a foothold they can multiply like weeds and start to
cause problems for you. A lot of people have a knee-jerk "kill it with fire" approach because, aside from multiplying like bunnies, they are also notoriously difficult to kill. If you scrape it off the rock, it will regrow. You may have smeared it around and created multiples, even. If you pull it with tweezers, the foot stays behind and it regrows. And so on.
There are a few ways to deal with this. Some are temporary, some are not. Injecting it with kalkwasser paste (as thick as you can make it) is probably the cheapest and easiest way to do it. You can also add a peppermint shrimp, although it's not a guarantee that they'll eat your aiptasia. You also have to be mindful of the species. Camel shrimp (aka dancing shrimp) are commonly marked and sold as peppermints. They are differentiated by the hump back and moving beak on camel shrimps, or the smooth back and fixed beak on peppermint shrimp. Berghia nudibranches are another option. They are obligate aiptasia feeders and will decimate any population you have in your tank, then die off. Your next choice is more permanent: a fish that will eat them. ORA and Biota both sell captive-bred
matted filefish that will eat aiptasia. They stay small, are unique, and aren't aggressive. Copperband butterflyfish also do the job, usually, but I wouldn't recommend them to an inexperienced reefer.
Best of luck!
