Can I clarify the best way to pay for US car hire?

I paid deposit with a UK GB£ card and received a bank charge for a foreign currency payment. It wasnt much but made me think Ill pay balance in US$

The price is shown in US$ I thought I would pay the balance with my US account debit card but guess what I received an international transaction fee even though it stated US$ and I paid in US$

Please can you clarify how payments are taken?