We have recently had a few merchants make the request about reversing a payment before it settles but after it's processed, unfortunately this can't be done.
The way our system works is that when a payment is initiated it cannot be reversed in flight. A credit card payment is instantaneous therefore obviously cannot be reversed, and while a direct debit payment from a bank account isn't instantaneous unfortunately we cannot recall the request once it's made. It usually (when the direct debit system itself is operating properly) takes up to 2 business days to receive a confirmation of payment, so you can't even process the refund back through our rails during this time.
In closing, once a payment is initiated, it has to go through to it's logical conclusion. A direct debit payment can't be stopped in flight, nor can it be refunded until it's completely processed.
You can however use the refund feature on the payment page which will avoid us settling the money to you after the payment is processed, expediting the process by up to 48 hours.