If a customer makes a mistake when placing an order, it is standard practice among online presences to cancel the order for the customer, and ask the customer to place a new order for the items they meant to order. I know it's always super helpful when online retailers are able to help cancel an order for me! Your customer shouldn't need to pay for shipping twice if you refund the first order for them.

I can definitely pass this feedback along - d​​​​o you have any examples of other web hosts that offer this kind of feature, @Auri?

Thanks Valentina, 

The issue is that they ordered something we had incorrect inventory of so it was our mistake that they were able to purchase the wrong item so it would make sense that the we should be able to amend the order from our end to remove any inconvenience to the customer.
We usually use Shopify for online sales and this was one of our first online orders with square. In shopify you can edit an invoice and request the balance from the customer via an email that is generated by the app.

It is possible to edit an invoice that's already been sent with Square, so long as your customer has not made a payment on the invoice yet, @Auri. I'm not sure if that helps in the meantime, but we'll be sure to update this thread if something changes in regards to the ways you are able to manage the fulfillment of Square Online orders. Thanks for the extra feedback here!