Blackbelt, the birds have already been paid for; the purchaser wants a refund. I think that a deposit for the carrier would have been in order; that way if it never returns, you have the cash to replace it. Although, since they came to you, why did they not bring enough carriers themselves? Not sure how many birds they still have to pick up, but is it enough that their cost covered the carrier? As pthers have said, the deal is already made; there are probably times or reasons why one would be willing to back out or undo a deal, but this does not seem to be one of those.
Worst case scenario for the seller, she re-sells the birds for a bit more than she purchased them for; shouldn't be too difficult.