A guild member used the RFI button to request an item from our bank. I used the RFI page to make the item as "delivered" yet it is still showing in our bank. Once I mark it delivered, shouldn't it be removed from the bank (unless we show more than one of the item)?

That's not something I've ever thought of. The bank was originally implemented using the WoW mod, and therefore didn't need to have any manual modifications, but since Lotro (among other games) don't support that, can see removing the item from the bank being a useful thing.