Currently, our integration with Square and Authorize is one direction. We push the payment information over to them, but we can't authorize refunds.
You'll need to perform the actual refund in Square or Authorize.
However, to get your business metrics to realign to reflect the refund, you can use the "refund" button next to the Payment received to note that you have processed a refund for that fee.
Note: Using the Refund button will not effect the invoice, just the payment received, so if you process a refund, you'll be creating a partial or unpaid fee. Adjust your Invoice accordingly to reflect why you issued your refund.