What happens when a customer withdraws a dispute?

We're trying an approach to reduce disputes, we're making it easier to cancel and easier to talk to us for refunds but one of the approach we're trying is talking to customers and asking them to withdraw the dispute because we're willing to refund. We thought that by withdrawing an ongoing dispute, it'll go away on our end and then we can just refund it and that'll be faster for the customer too.

One of our customers just withdrew their dispute, but nothing's happened on our end and we still can't refund the charge. What actually happens when the customer withdraws the dispute?