In order to delete a payment from an invoice in Cutting Edge, first you go to the invoice and click the arrow next to the payment in the invoice items box:

From the payment screen that opens, click the delete icon in the top right and confirm that you wish to delete the payment

Your payment should now be deleted from the invoice

NOTE: Clicking the delete icon on the payment in the invoice items box will not work, this process is the only way to successfully delete a payment from the invoice.