I've never directly asked to look at a teller tray. Most of the time I just take a peek from across the counter. I have had some tellers actually show them their tray to see if there was anything I wanted. I usually tell them I'm looking for anything old.
I never Really ask to look through their tray. I just ask for any Halves and Large dollars, and then I add them to my dump pile. I have had a teller offer me to search the tray so from now on i'll just edge search any dimes quarters and halves.