I did what a poster above did last week and here is how all the charges got handed by United and AMEX.
Bought a ticket with non-AMEX Platinum card, then added pet to both flights, for a total of $250, on AMEX Platinum. Canceled ticket later that day, at which United gave me the option of having the amount reimbursed to my card that I charged the base fare, or a travel credit. I choose to refund all the amount to non Platinum card. Now the two $125 charges for the Pet fee posted to my AMEX, then United issued credit to the Platinum card. So they didn't credit the card that I bought the base ticket on. Then I was like, oh well... However, I checked my AMEX statement Tuesday morning and AMEX issued me 2 credits in the amount of $125, and $75, even though United had issued credit for those pet charges.
So I don't think that AMEX will claw back the $200 United credit, but if they do, then I'll just do what I did, and take the travel credit when I cancel the ticket.
All in all, the above method works!