I like the way PizzaPirate rolls on this one. The realtionship with the customer is the bigger picture. Don’t be a doormat and give them a free pizza, but making an offer to discount a second pie makes good sense. You get a partial sale and potentially keep a customer who orders. A written policy would also help make things clear for everyone in the shop how to handle it all.
I do know that it is always tricky to take phone orders 10 minutes before closing. I hate to lose a sale, we are nearly always there at the shop until 30 minutes after close of front door . . . but I hate to get a no-show at end. They truly are so scarce that we just take the order and make it clear we need them there pretty quick. Really, we are only about 10 minutes away for vast majority of customers.