Unfortunately this is a big flaw in Square's invoice setup that many of us have requested fixed. Basically you only have a couple workarounds once a deposit is paid on an invoice. One is that you can send a link by email to the customer which they then have to go through. It's not the invoice per se.
The other is to take the balance, ring it up like a separate sale and then go back to Square and marked it 'paid by Square' so that it doesn't double your end figures. I forget whether that last step is done on the PC virtual terminal or on the POS. Hopefully they address this soon as it is a pretty big hole in the functionality.
