If you have invoiced for the work undertaken so far then, ideally, I would recommend paying off the invoice as it will otherwise become overdue. Unless you have taken manual action to prevent it this will cause reminders to be sent automatically, also if you send the customer a statement it will show as unpaid (statements don’t show money held on account).
As the customer, presumably, has a link to the invoice there is a risk that they will go back and check. Most don’t but there are one or two who will.