As an admin you may want to only refund a certain amount or percentage of a payment.
To partially refund a customer:
Find the relevant payment in the Invoices table
Click on the Actions button
Select 'Refund payment'
Edit the refund amount as required, and choose whether to also cancel the invoice and/or appointment
Tick 'Suppress mail' if you don't want the customer to receive an email notification of the refund