This is also a common problem with Peppermint Shrimp and Hermit Crabs which are added to eat Aiptasia or nuisance algae.

From what I have seen in the hobby, the most common reason the animal will not eat the target live food is because
there is so much other tasty food in this new home already or
the hobbyist is supplementing so much tasty food that
the animal has no need for the Aiptasia or algae. In this kind of situation, the first thing I do is severely curtail or even stop feeding for several days or even a week if possible, to see if hunger will entice the animal to eat the target pest. This seems to work most of the time for me, but if it doesn't work, keep reading.

I've never had to resort to using a Filefish, but here is what I do if I have strong doubt that the Peppermint Shrimp may not eat Aiptasia or that Hermits may get distracted by some other food.
1. Fill an appropriate size bucket or small bare tank with tank water. (1/2 - 5 gal)
2. Place a loose rock with the target Aiptasia or algae into the bucket.
3. Place the shrimp/crab/filefish into the bucket.
4. Periodically check to see if all the target food has been eaten.
5. Daily refresh some water from the tank and keep the water temp at between 70-80 degrees (set the bucket
off the floor where it may get too cold. I typically don't bother with a heater, but that's just simple me.

In this small container I typically don't bother with circulation, but if that's a concern, I use an air bubbler only.)
6. Do not feed the bucket.
Sooner or later, usually within 2 days, hunger will drive the shrimp/crab/fish to eat the target food on the rock. The animal will then discover that the Aiptasia/algae is good food.
Finally, return the animal to the aquarium, OR to ensure a stronger connection, repeat a second time with another rock.
Aloha