This can be done either in the admin console or through our API.
In order to process a refund in the admin console, open the invoice and from the invoice actions select "issue refund". From here, you will be given several options regarding how you would like to refund the invoice and how much of it you would like to refund.
From the api, use the "Refund an Invoice" endpoint. https://developers.recurly.com/api/v2021-02-25/index.html#operation/refund_invoice
There are more granular options from the api and they are described on the documentation provided.