There are two good ways of dealing with the situation
Compromise it and move on. This will invariably happen to everyone in the biz and the proper thing to do is let them have their cake and eat it too, literally!
Don't comp their meal. Instead of comping their meal, give them a gift certificate in the amount of the entree. That way they will have to return and will most likely bring at least one other person with them. Not only have you taken care of the problem, but you are also bringing in potentially new business when they return.