Have you got a picture of the caterpillars?

welcome to GoY.

a photo added to your question would certainly aid the id process. There are many hairy caterpillars so difficult to id.

Alstromerias are tough and will stand a few caterpillars. Unless they are rampant I would leave them alone. It would be a pity to destroy butterflies or moths which are already under threat. Hairy caterpillars sound interesting! At least you know they are not cabbage whites or sawfly! You could google hairy caterpillars USA and try to find a match!

If you are actually in the U.S., you could use spinosad or B.t..