I feed my tank frozen foods twice a day, or broadcast feed. So my BTAs mostly get fed that way, I don't target them. Rarely, when the mood takes me I will add things like brine shrimp or mysis or lobster eggs directly to the anemones tentacles. I prefer to feed them smaller, mushier foods and I NEVER see them regurgitate anything this way.
They will also take algae IME and show a feeding response to glass cleaning on occasion. I don't deliberately feed it to them but just my observations since keeping them for the last 4/5 years.