I think I would just 'enjoy' the fact that you caught her out and see what transpires and say nothing. If she comes back, you can enjoy a quiet personal snigger.
Some of you guys just kill me with your attitude which always seems to be: Sack the client or saying your better off without, or that you hate clients who are like this, don't fit them in if they come back, drop her .... listen to yourselves! What kind of a way it that to run a business? Sure clients like this are a pain but they pay you for a service ... they can be a pain and we have to put up with it because that is life and it's our job to provide the service they are paying for even if they are moaners and wingers.
I can just see it all. She goes in the salon to find she is early ... thinks she'll blame Carl rather than admit that she could be to blame, whatever ... it has thrown her day out, she says she'll come back. she swans off up the street and sees another salon, thinks ... I'll just see if they have room for me NOW .. they do! she sits down and rings Carl to tell him she is not returning that day (she's got what she wanted). So typical. I suppose you could say at least she had the courtesy to let Carl know.
People are people and it takes all sorts. It would be nice if everyone were lovely and thoughtful and courteous but that just isn't the way people are and when you are in a people business you take the rough with the smooth.
It isn't personal, Carl. She just wanted her nails done then and there and got lucky (she thinks ... mwah mwah).