Intuit's payment processing does not utilize an alphanumeric zip code field. It is up to the credit card holder in conjunction with their credit card issuing bank, to provide credit card information that would be compatible in the U.S. for processing.
For transactions that have problems due to such a zip code situation, your customer will need to contact the card issuing bank to determine if there are options for using their international card with U.S. based businesses that require a 5-digit numeric zip code.
If you feel the proper information has been obtained but there is a question whether a card is being declined due to being an international card, A Voice Authorization may be performed for verification and captured in the Online Service Center (Merchant Center-merchantcenter.intuit.com) if successful. However, if the card fails the voice authorization, your customer will need to speak with their card issuing entity for more information and submit a different form of payment.
If you have any further questions, please call QuickBooks Merchant Services at: (800) 558-9558.