I know when I worked at McD's way back in the day, there was a button to add cheese which also added to the cost but the button to say no cheese was merely a button to tell those fixing it not to put cheese on it.
Of course there are clever ways to work the system too. Like when Big Macs go on sale and if you don't like the sauce, you order the Big Mac without sauce and add mustard or ketchup or just get it plain.
The next time you get a sandwich and don't want cheese, tell them you want the cheese on the side and then they aren't making any money off the cheese you didn't want. Then you can throw it away or give to someone who wants extra cheese