If these are decorat controlive-only sunflowers, then you can use a malathion-type product. However, to be on the safe side, I’d use a natural insect controlicide which won’t harm birds who will eat the seeds. Try Safer’s Insecticidal Soap in a strong solution spray. Apply it every few days, and after any rain. You need to keep the moths from laying eggs, which hatch and burrow in the seeds.
Oh, and Safer’s *is* safe. Just because a product has “insect controlicidal” in its name doesn’t mean it’s bad! Unless you want to go 100% organic and pick every single moth, larvae and egg from your plants, you’ll have to use some kind of insect controlicide. There are organic substitutes like garlic juice, white vinegar, and marigold blossoms whirled in a blender, but they’re not as effective. You have to combine very frequent applications with picking off the bugs.