Hello circulation.

Welcome to the forum.

"For every [X] you get [Y]" means that every time you do X, you get Y.

I would understand this:

"For every week you rent one of our cars, you get 2 entire days free of charge."
to mean that for every week you rent a car, paying the full fee for that week, you get two more days for free.

If the fee is $100 dollars a day, then it will cost you $700 dollars to rent the car for a week. After that you will get 2 more days for free. You will get a total of 9 days for $700.

That is what the grammar tells me. However, the wise thing to do is to check with the company to ask them whether that is what they mean. They may have something else in mind.