Just the movement of him offering the card to her makes her take a jerky step backward-- in those heels it is fucking miraculous that she's not only managed to run at full speed but that she hasn't fallen over out of shock yet-- And she just stares at him.

This is not her father. This person, if he is in fact a person, does not even know who her father is. If he knew, he would have recognized her right away. (She has been told that she looks just like him.) She wouldn't have the first clue who John is, either, and she opens her mouth to say so, but the words don't come, because who cares? Something deep in her primordial brain tells her Run, and she does.

She makes sure to kick him in the shin first, though.