Two different things get confused here, and only one of them is yours to handle.
A refund is you giving money back: a duplicate gift, a wrong amount, somebody who asked. A dispute is the giver's bank reversing the charge without asking you. They work nothing alike.
Refunding a gift
Find the gift in your giving list and refund it. The money goes back to the card it came from, and the donation is marked refunded so it drops out of your totals and off that person's giving statement.
A gift can only be refunded once. Trying again tells you it is already done rather than sending a second refund.
The warning about money already paid out
This is the part worth reading before you need it.
Gifts do not sit in Stripe indefinitely: they pay out to your bank account on the schedule you set on Bank & Payouts. Once a particular gift has been paid out, refunding it does not pull that money back out of your bank account. Stripe refunds the giver from your Stripe balance, and if that balance is thin the shortfall comes out of your next payout.
If the gift went out in a fund payout run, the app stops and warns you before you refund it, and makes you confirm deliberately. Gifts paid out on your regular schedule don't trigger that warning, so check the gift's date against your last payout yourself. Refunding is sometimes exactly right, but the money movement is not what most people assume, and finding out afterwards is unpleasant.
If the amount is large, talk to whoever handles your books before confirming.
Refunds cannot be undone
There is no un-refund. If somebody refunded the wrong gift, the only remedy is asking that person to give again. Slow down on the confirmation step; it is the one screen in giving where a misclick costs real money.
Disputed gifts are different
A dispute (a chargeback) is when a giver contacts their bank and says they did not authorise the charge. Usually it is somebody not recognising the name on their statement rather than anything fraudulent.
You cannot respond to a dispute from your account. When a donor's bank opens one, we email your church's admins to tell you which gift it was, and our team reviews it and responds on your behalf. There is a deadline on responding to a dispute and it is short. The disputed amount is held while the bank reviews it.
So you do not have to do anything when that email arrives. But if a giver tells you they have disputed a gift, or their bank has contacted them about one, it helps to email us with the giver's name, the rough date and the amount, and a quick personal note to the giver from the church often clears up the misunderstanding sooner than the bank process does.
Do not refund a gift that is already disputed. You can end up out of pocket twice: once for the refund, once for the dispute.
Reducing them
Most disputes are recognition failures. The single best prevention is that the name on the card statement looks like your church: check what yours says in the Card statement name card on Bank & Payouts. If it reads like something unfamiliar, change it there (on a church's own Stripe account, that means through the Manage bank & business details panel). A giver who recognises the line never calls their bank.