This is business. What you find petty, I find necessary. As a business, if you want something to stop, attach a fee to it. It's an effective way to stop a behavior pretty quickly!
And yes, I charge for every minute a parent is here past their contracted time. I tell every family to make sure they arrive with plenty of time to gather what they need, physically and verbally, THEN sign out. I don't think it makes me any less of a caring person or caregiver just because I demand overtime if they use my free time.
Even 5 minutes a day adds up... that'd be over 21 hours a year you gave away for free.