A bandage for protecting a wound site in the extremity of an animal such as a dog or pet, has a body in the form of an inverted cup with a transverse wall and one or more access openings therein, a lip on the cup to fit against the animal's fur around the wound site, and a cover piece to enable selective covering of the access opening. The cup has a roughened exterior surface texture that is extremely irritating to the animal's tongue or lip, wherein the animal is discouraged from continuous licking and/or chewing on the body, and thereby inadvertently dislodging it from the wound site.