Is it OK to have someone else pay for your (United) international flight change fees using their credit card?

I'll be travelling to the United States from Egypt in a few days on an exchange program. A round-trip United Airlines ticket has been booked for me through a travel agent.
I'm planning to extend my stay for a few days to visit DC with my cousin, so I asked the travel agent to change the return flight. He replied with a change fee of 385$ which is 200$ above what is shown on United.com.
Upon confronting him, he said has to up-sell to avoid having me ask to change the booking again. And suggested that I make the change online.
Which is what I tried to do. However, I could not pay using my debit card as it turned out United does not accept payments from Egypt.
Luckily, my aunt has offered to pay using her American credit card. However, I've been warned that some airlines ask passengers to show the card that was used to make the booking before boarding the flight.
I sent a support request to United a few hours ago, asking if I can have someone else pay for my change fees and they haven't replied yet.
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Can you change a United flight or is it just a credit?
You can adjust your travel plans without any change fees \u2014 including for award tickets \u2014 for flights within the U.S., or for international travel originating in the U.S. This applies to most United Economy and all premium cabin tickets. You'll just pay the fare difference if your new flight is more expensive.Can you transfer airline credit to another person?
Travel certificates are not transferable and may not be sold, traded or bartered. However, the original recipient of a certificate may arrange travel for another person if done without selling or bartering the certificate.Does United allow name changes on tickets?
In United Airlines, you have the option to correct a misspelt name. The changes to a name in the confirmed itinerary is done according to the name change policy of United Airlines. In this airline, you are allowed to make several changes and the name change option is one of them.How can I change my flight without being charged?
6 ways to avoid paying an airline's ticket change feeTop Three Ways to Redeem Your United MileagePlus Miles | To The Point | Ep 20
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