Payment Requests: What your customers see
When your customer receives your payment request, they will see a request to pay the balance owed on the edited order–what we call an adjustment order.
For example, you edited an Order #1001, resulting in Order #1001A, your customer will receive a payment request with a single line item Balance Owed on Order #1001A which will be listed for the amount due as a result of your edits. This adjustment order's line item is marked as non-fulfillable and non-taxable since it will be applied towards Order #1001A, so other order management or fulfillment apps should not have a problem with it.
Next your custom just needs to click on the "Complete purchase" button to be taken to the Shopify checkout for your store. From there they just need to pay using their credit card as usual. All their information will have been already populated except for their credit card.
When the order is complete, they will receive a confirmation email and you will automatically do all the bookkeeping of joining all the transaction data together, marking the adjustment order as fulfilled and archived, and marking the edited order as paid.