Not sure if you asking because the anemone is a pet and you dont want it hurt or its a pest and you do.....
Many fish will/can eat/pick at anemones. To many to list seperately. Some are some of the angles, butterflies, batfish, triggers, filefish......
An anemone will catch and eat any fish that happens to allow it to happen. Thats what they do......Many timid species often end up consumed are gobies, blennies, manderines and any small enough fish that is spooked and flees into one.