.....kinda missing my point chaps, here goes..
...offering to pay for the damage; sophet plus exhibit gnome a isnt what the customer wants, because as we know the customer is lying about the damage and wants to save face in cancelling the service, so....two possible solutions to get the customer to admit why she no longer wants the service...
1) Massive slanging match.
Result; her position is essentially re-enforced whilst you lose your rag and get frustrated, nothing is achieved.
2) I'm so sorry about the gnome and the sophet Nora, to my knowlede that damage was not due to either me or my employees but I'm happy to rectify that damage regardless of cost to myself if it means we can stay friends and I keep you as a customer.....
Result: she still has a window cleaner she cannot afford and will be forced to tell you so. If she keeps you on you can cancel at your leisure, no harm done.