Sandra is correct. If you notice in the screenshot most of the other expenses have the green AMEX icon. The one you highlighted does not. What you are seeing is the e-receipt and hotel itinerary item. These default to cash unless they get matched to the card charge. So, the employee needs to let those items sit in Available Expenses until the card charge comes in and matches. That is the only way you can get the payment type to change.

I don't know how you are set up, but employees should not receive reimbursements for AMEX charges. They submit those and then a payment is sent to AMEX to pay off that individual's statement or maybe you are paying the entire statement received from AMEX. However, if you are setup where your AMEX cards are Individual Billed/Individual Paid, then the employee would receive funds to pay off their AMEX card. It's difficult to answer/provide help not knowing how your system is setup. However, it appears you want employees to pay for Hotel on the AMEX card, if that is the case, they need to make sure the AMEX charge has come into Available Expenses. The green icon is the most important.