Tragically, there's absolutely no need to exterminate this monster, but if they try, it won't be pretty. Instead they could just "sacrifice" one woman with big breasts. She wouldn't even be harmed, let alone killed, and would be able to return just fine. An erotic dancer, for example, would be a perfect sacrifice. But a waste of skin noble with too much pride can't think outside the box.
Of course there's a chance they accidentally find a totally different monster, which actually behaves like a monster. There seem to be those hanging around.