If they're in the compost, they eat only dead stuff. Don't have a clue which moths might do that?

Is it possible to post a picture of the critter?

While I have seen moths flitting around my compost piles they do not grow there since the larva of moths need live plants to grow on. There are a number of other insects that will lay eggs that will hatch and become larva in compost but they would not be identified as moths, normally.

Adult moths are not going to eat any of your plants although they do live on the nectar the flowers produce. The larva of moths will however eat many plants, but you need to know which ones are pests and which ones are beneficial before taking steps to control them since you can do more harm than good with the wrong approach.

kimmq is kimmsr