It is extremely unlikely that this is anything to do with AA or any US-based merchant. Rather it will have to do with the use of a debit (or perhaps better put "non credit card") for an overseas transaction.

You may find this to be even more true should you use a debit card at a hotel or for a car rental. Those facilities will sometimes place holds for not only the anticipated charges, but to protect themselves in case of damages as well.

Your transaction is processed almost as though it is a check. AA almost certainly released the "hold" immediately (typically in <1 hour). But, it can take the banking system which will include at least one bank here in the US and one or more banks in the UK for the hold release to make its way to your account in the UK.

The advice above is sound for more reasons than this. You have far greater consumer protections with a credit than a debit card, not the least of which is that at the very absolute worst, you are on the hook for a bit of interest when things need to be sorted, rather than having your funds tied up.

AA is doing you a substantial courtesy by providing the letter, but it appears that your own bank has handled the issue.