The accounting definition of a refund is an amount of money that is given back to the customer.
You have two ways of refunding a transaction.
HiPay Backoffice
In order to refund a captured transaction you should go to the Transaction Preview.
Here, you have a capture button, click on it to do a manual refund. You can refund a transaction fully or partially.
API Request
In order to refund a captured transaction you need to use the maintenance API.
Full refund: you can only send the parameter operation set to refund.
Partial refund: you should send the parameter operation set to refund, the amount you want to refund and the currency.