Like many bug-based additives, this red dye used to be listed as just another "natural color" on ingredient lists. But since some people are allergic to cochineal insects, the dye is now listed separately as carmine. Because people can find it in an ingredient list, they sometimes get a little grossed out by its presence -- or demand its removal. In 2012, Starbucks stopped using the dye after complaints.
But carmine isn't cause for concern in most people. From Live Science:
Aside from its role as an allergen, cochineal has no known health risks, although those who keep kosher or choose not to eat animal products will want to keep their distance. In addition to food, cochineal is used as a dye in cosmetics products, including lipstick, and at least one person has reported a severe allergic reaction to a cochineal dye used in a pill coating.
Reactions to carmine seem to be severe, but extremely rare. So unless you're allergic, just enjoy your buggy treats.