They're on the hook for the finance, if you're leasing. If you're talking about a short-term rental to pootle around in for a while: they're on the hook for th

They're on the hook for the finance, if you're leasing. If you're talking about a short-term rental to pootle around in for a while: they're on the hook for the car itself, because that's now a car they can't rent to someone else. If they weren't on the hook for anything, there wouldn't be much of a business.