For example, eat it on the first order to validate the payment method and reduce a bit of risk. Then on subsequent orders, don't bill the card immediately. Allow the customer some amount of credit based on e.g. how many previous orders they have paid for successfully and the age of their account.
Once you've reached your threshold for whatever amount the user is allowed to buy before you bill, you then bill the card and send a receipt with the orders you've just charged for.
This will take some work, but it will reduce the friction of users seeing that fee on checkout.