There was a deli in Dorchester (part of Boston) when I was a kid back in the 40s and 50s that used these tickets. The countermand/server would just punch the total due and you would then pay at the cashier.

Katz’s uses them for two things. First, each person is given one on entering and has to turn it in when leaving. They no longer punch the amount due (obvious reason) so they just hand write the amount on the back. The cashier adds the tax on the way out.