Ten Types 
Order the Book
"Read them the riot act."
YOU: Listen, I get that we blew it and you are upset about your luggage. But there are only two people standing at this counter who care about getting your bags back................ and one of them is quickly losing interest.
CUSTOMER: Sorry. What do you need to know?
R&R: We actually saw someone do this successfully at a luggage counter on 20th century Earth. She was totally sincere in her tone and expression. Had there been any sarcasm or even anger it might not have worked. Note that in your response you first made two acknowledgements of what they told you; 1) that your company blew it and 2) they are upset. This is backtracking. It lets them know they are heard. You then lead by pointing out that you and they were on the same side with the statement: "two people at this counter care about your luggage." That acknowledged that you both have the same intent . Then by saying, "one of those people is losing interest" you pointed out their behavior was defeating your common purpose. The advantage of dealing with people in the Tank mode is you can be blunt and direct with them. A dangerous but well played move on your part. We you. However, we are not going to let you get away that easy. Go back and try another approach that is a bit safer.