How do the people on Impractical Jokers get brand-name places to allow them to come in and act stupid and bother their customers?
To be clear they do things that a person could press charges over. Touching, saying perverse things, etc
The simplest answer is that in the early days of the show, while they needed permission to enter the stores, they were largely left to their own devices to do the actual comedy (hat tip to @walt for the quote link)
Q. Do you need permission to go to stores and malls?
A. Oh yeah, clearance is necessary, but once we are there; they leave us alone and just let us blend in without blowing our cover
Now that the show is more popular, the owners are aware of the likely consequences and actively welcome them in via their producers:
Q. How do you get permission to get into all these places like dentists’ offices, businesses, fast food joints ... ?
A. We have a team that that sorta reaches out — I mean it’s a lot easier now because we have people that are just fans of the show, so they want us there.