I don't do drop offs....but if I were in your shoes I would leave 10 minutes early one day and not be there when they tried to drop off. Bet it wouldn't happen again! That's just me though, I don't tolerate nonsense.
I would do a face to face for sure. Make it very clear that it is unacceptable and you will not take the child if they are not ready to go. You have to then follow through. If you allow them to do it they will continue to do so.