Thanks for dropping by and elaborating on your concerns, info2217. I have some clarifications to provide regarding the duplicate payments associated with the deleted invoice.
The payment (£80) shows twice on the Bank transactions when applying to the Invoice (£40) because of the balance left (£40). That's why both transactions will show as linked to the same invoice.

Once you delete the Invoice, the payment on your Bank transactions should display the whole amount (£80). If not, please reload the page to reflect the changes.

Since the outstanding invoice is £40, the remaining amount (£40) will serve as a credit for your customer. You can use this for the next one. Picture this: the first half payment is for the initial invoice, and the second half payment is for the future invoice.
Here's a reference to learn how to void, edit, or delete settlements: Record invoice payments in QuickBooks.
Return to this post if you have other questions about managing invoices or customer overpayment. We'll be here, ready to help you.