Great, they're bantering and at ease and making a good impression on the stranger, that means she's on top of things.
Normally she charges for this kind of thing but knowing about a new cape in town is valuable to her (and to Coil). Not doing this was kind of the favor she owed him, but if he asks for it?
Come out and play, power. Does he have the metaphorical equivalent of mud from a particular Brockton Bay alley on his boots?
Not from Brockton Bay.
Which direction did he come from, then?
Not from the south. Not from the west. Not from the north. Not from the east. Not from direction. Not from -
She cuts it off. Her power does get things wrong sometimes. But it follows specific clues, so -
'How do I know he's not from any of those places?', she tries asking her power.
Voice, accent, mannerisms, word choice, clothes, skin, hair, fingernails, complex phenotype -
Huh, her power seems to think he looks wrong (or at least not local) in every possible way. He doesn't look weird to her - he's definitely pretty but not in a 'real people don't look like that' way. Her power is definitely picking up on something, but she hasn't met enough people like him or from the same place to pin it down.
Actually... why is he wearing a cloak? She wrote it off as part of a costume, the proverbial cape, but if he just triggered where did he get a cloak? And his trigger messed with his memories, so maybe -
Power, did his power change how he looks or behaves or his clothes?
Powers affected clothing. Affected looks. Still affects looks, ungoing, unconscious, uncontrolled. Affects cloak. Affects clothes. Affects height, eye color, mannerisms, face, features, attractiveness, voice, tone of voice -
She cuts it off at the first twinge of a headache.