Answer:
What you describe Is a "band-aid" that banks sometimes use to avoid inconveniencing the customer. However, please understand that it is completely of your own design, not something the law would require or even allow you to do. In other words, you made this solution up. Having made it up, you can set your own boundaries and you should tell your customer where they lie.
For example, we will pay your outstanding items for XX days. If you find there are some outstanding after that date you must describe them to us in order to facilitate their payment. (Yes, I'm well aware that most people will not be able to do that, but that problem has their brand on it, not the bank's)
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