It is really great how it shows you exactly what can be placed into your warbank/ warband bank from your inventory. When the warband tab is open and you have your bags open, the items that can be placed will be selectable and those that cannot go in the warbank will be greyed out.
I am suggesting the addition of a filter toggle button in the normal (and reagent) bank tab, that will basically apply this same filter. Showing you what is inside your normal bank that can be moved into your warbank.
As for now, the only way to see this would be to move stuff from your bank into your bag so this filter is applied. Which just seems like an unnessacary and inefficient extra step.