Request, in writing, refund of unused tickets
First, it sounds like the original tickets were Business Class. So, hopefully, they are fully refundable. Next, you should contact the ISSUING AIRLINE for your tickets. If American issued the tickets you should contact American about a refund, and not Cathay.
The ticket numbers for your original tickets, and their replacements, should appear on your credit card statement. Make sure you quote the ticket numbers of the ORIGINAL tickets, and not the replacements.
If you live in the USA you should mail your refund request, by certified mail with return receipt requested, to the address for refunds which American, or Cathay, provides. Keep copies of your letter and save the return receipt.
If, after 30 days, you've heard nothing you can try disputing the cost of the original tickets with the issuer of the credit card you used. If that fails then you may need to take American, or Cathay, to small claims court.
Good luck!
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