Can I refund a customer's purchases?

That depends on the Bancontact Pro solution used to accept the payment.

For payments made via the Bancontact Pro sticker solution or the Bancontact Pro payment app: you can refund the amount to your customer. There is no way to initiate this automatically via your payment solution.
For payments via the Bancontact Pro integrated solution: your payment system provider can explain this option or add it to your payment system.

Are you a provider of Bancontact Pro payment solutions and would you like to offer this option? If so, please visit our developer platform.