Shortening sessions to avoid late fees

Howdy.

This morning I had a client late cancel a session within a few hours of the appointment. I sent the email stating that since we could not reschedule (I was full the rest of the day), a late fee would be charged. Someone requested the appointment slot once it opened up, cool. But then the client emails me back and asks if, to avoid the late fee, they could keep the session but leave 20 minutes early.

It's been handled and addressed, but I'm curious to hear how others would have responded to the request to intentionally shorten a session so the client can avoid a fee?