Why does the landlady want billy to sign the guest book

The man thinks she's the lady he's trying to find. she then lifts the veil and he announces that he'd made a mistake and that he'd thought she was the woman, but had been wrong. truthfully, though, he'd been right. this reveals that the he didnt recognize her (though he said he would recognize her voice or her build) and that he's still looking for the girl. he doesnt find the woman appealing or attractive, and is more or less disgusted by her appearance. he didn't understand what the lady meant when she told him the story about her "friend"