You can issue a partial or full refund on an invoice the same way that you refund a regular order.
From the main menu navigate to Selling » Orders
Locate the invoice that you'd like to refund, and click on your customer's name
Scroll to the bottom of the order details page
Click the Send Refund button found underneath the order totals area
Fill in the refund details, including the amount to refund and a small note about why the refund is being sent
Click the final Send Refund button to complete the refund process
Once the refund has been sent your clients will see the refund on their credit card within 2-3 business days.
Note: Invoices and Orders can be refunded up to 90 days after they were paid. After the 90 days you will need to make the refund from your end using a check or some other means.