can leaving method antibacterial cleaners sitting on counters (granite, stainless, etc.) do any damage i.e. discoloration? Does it strip any polish/finish?

as with any cleaning product, you should always test in an inconspicuous place first. these products are designed to be used on hard, non-porous surfaces. some surfaces, such as granite, wood and certain types of tile are porous in nature. if you do have these types of surfaces, be sure they are effectively sealed prior to use.