Short answer: No.

Another great thing about our integration Stripe is that there are no additional fees for online refunds.

The one thing to keep in mind is that if your client had initially paid the processing fees, you will then have the option of either paying the fees yourself and refunding the client for the processing fees or leaving the fees charged to the client.
To put it simply, in the end either you or your client will need to pay Stripe's fees if your client initially paid the fees.

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