Shipping refund claw-back

A customer placed an order on my FBM listing and paid $12 for UPS Second Day but carrier took 5 days. Customer messaged a request to have the shipping refunded, which I politely acknowledged and provided using the Amazon ‘refund shipping’ process, giving reason as ‘carrier late delivery’

Anybody know if I can claw that $12 back from UPS or AMZN? The shipping label was purchased from Amazon so I don’t have standing to request a refund direct from UPS.

Is there a workflow tucked away somewhere in Seller Central for this, or do I open a support case? Or do I eat the loss?

I’m not terribly concerned about the $12, but I would like to learn the policy and process.