I wonder how they are going to prove they got rid of the gryphon if Annette just talks it into relocating somewhere else? Of course other folks can go the mountain and not find the monster, but just once wouldn't be enough. For all they know, the gryphon could be merely temporarily elsewhere, like busy eating something somewhere, and wouldn't be back in a few days. That's why adventurers need to bring back unmistakable body parts. In fact if they told they did beat the monster, but it escaped, the townsfolk would still fear the beast would simply return a week later.