What's the 411 on her? My knowledge of Japanese monster lore is sketchy, and she sounds like a delightfully creepy monster figure.
The basics of a the story is, a woman, wearing a veil, or a surgical mask*, will randomly approach people on the street, and ask them 'am I beautiful?'
If they answer yes, she removes the veil/mask, and reveals that her face has been sliced, from the corners of her mouth, back to the ears, and she'll ask again.
From this point on, there's multiple variants.
In some versions, it doesn't matter what you answer, she'll slice you up. In others, if you say yes, she'll let you go, because you've assuaged the fear that turned her into a malignant spirit in the first place. Sometimes, if you say 'yes', she'll seem to let you go, but follow you home and kill you there. In other versions, you have to confuse her by saying 'you're average', or utter nonsense, like 'pomade, pomade, pomade'. Some versions say you can distract her with candy.
Saying 'no' is never a good idea.
Her origin story boils down (again, there are variants, but these details hold) to her being a beautiful woman, with a jealous lover. In a rage - over being cuckolded, or simply having another man look at her - he takes slices her mouth open, to mar her beauty.
* The mask isn't that big a deal in Japan - it's not uncommon to see people wearing them on the street, because it's considered polite to do so, when you're sick.