Q: I am hoping that you can resolve my issue with American Airlines. I recently booked four airline tickets on the American Airlines site from Buffalo, New York, to Miami.

I had to change my flight, and an airline representative told me I would be charged a fee but would be refunded the $2,410 price difference. I was perfectly fine with being charged the cancellation fee.

I asked to be emailed a copy of the changes so that I could have a hard copy. The representative said I would have to call back after the flight for a receipt. I found that strange and asked her for assurance that I would be able to get a receipt. She assured me I would.

I called back after the flight to get a copy of the receipt, and it was a headache. I then checked my bank statement to see if American refunded me the difference. It didn’t.

American Airlines owes me $2,410. I don’t understand why the airline was so quick to charge me additional fare and take it from my account but can’t give me back the difference. Can you help? — Ahlam Shahbel, Toronto

A: American Airlines should have promptly refunded the money, as promised. Actually, it probably shouldn’t have charged you a change fee at all, since you made your changes within 24 hours of making the reservation.

American Airlines has a 24-hour rule, mandated by federal law, which requires it to fully refund most tickets within a day of purchase. Since you were making your arrangements for domestic travel, that rule should have applied, even though you reside in Canada. But that isn’t the real problem here — it’s that the airline offered you a refund but didn’t follow through.

You were smart to try to get American’s promise in writing. When the airline representative didn’t offer a receipt or a written assurance, you were right to be skeptical. I can understand why you would check with your bank after getting only a verbal promise. After all, when it comes to airlines, talk is cheap.

In a case like this, you really need to take your appeal up the chain of command. I list the names, numbers and email addresses of American Airlines’ executives on my consumer-advocacy site: http://elliott.org/company-contacts/american-airlines/.

I contacted the airline on your behalf, and it turns out there’s a little more to this story. Part of the fee you paid was for your seat assignment, which is nonrefundable. But you were due a refund for the fare difference on your four tickets. It’s not clear why American hadn’t sent that yet, but after I reached out to the airline, it did.

Christopher Elliott is the ombudsman for National Geographic Traveler magazine and the author of “How to Be the World’s Smartest Traveler.” You can read more travel tips on his blog, elliott.org, or email him at chris@elliott.org.