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Keep in mind, it’s called a foreign transaction fee, not a currency conversion fee (though some banks might include that too).
Even if the charge is in USD, if the company processing the payment isn’t based in the US, you’ll probably get hit with the fee.
That’s why when overseas point-of-sale systems give you the option to pay in USD, it’s a bad idea.
Not only is the exchange rate likely to be bad, but you might also end up with foreign transaction fees despite trying to dodge them.