I have posted on another thread about detaxe refund after paying with non-Euro AMEX. Hermes detaxe is with global blue & they have an agreement with AMEX that all refund will be made in UK pound first before converting into your AMEX local currency.
My example was: I paid my purchase at FSH in Euro. When Hermes Global Blue issues the detaxe credit, the amount will be converted from € to £ based on the day the process the refund after receiving the stamped document. On my AMEX statement credit I can see the £ amount listed in the details & AMEX will covert £ into US$/Cdn$ local currency. Thus, two or more foreign exchange transactions which may result a different refund amount.
If you pay with Visa or MasterCard, Hermes Global Blue will refund € directly. I wish I know earlier & not losing $ on the refund.