Let's say you need a refund, but you no longer use the card that DistroKid originally charged. Where does the refund go? Great question!
It varies by bank. If you have another credit card account with the same bank, sometimes the bank will apply the refund to the your other card. Sometimes, they'll send the funds to your bank account, or apply the refund to any outstanding balance on the card (it should still appear on a statement, however, if this occurs.)
Other times, your bank may send a paper check. And sometimes, the funds sit there for a long time until you contact your bank to request the funds manually.
What doesn't happen is the refund automatically going to whatever other card you have on file with DistroKid (unless it falls into one of the categories above).
TL;DR: Ask your bank.