Conference Joy uses Stripe as our payments partner. After logging in as the admin of your conference, click on on the Payments link in the sidebar. Confirm you're using Conference Joy's online payments feature and click on the 'Manage your Stripe account' link and you can issue the refund from the Stripe interface.

Note that the transaction fee is NOT refundable; Stripe charges Conference Joy a fee for every transaction and you will not be able to remit that. The most you will be able to refund your guest is the actual payment that you've received.