You are right to be concerned about the appearance that your charity may become involved in a political campaign, because a 501(c)(3) organization that intervenes either for or against a candidate in a campaign for public office can lose its charitable exempt status.  But it doesn’t sound as though this situation should get you in trouble.

In its most extensive recent guidance on “electioneering,” the IRS has made it clear that it looks at all of the “facts and circumstances” to determine whether the charitable organization itself has taken action in some official way to support or oppose a candidate.  (See Ready Reference Page: “IRS Issues New Guidance on Electioneering”)  In its Revenue Ruling in 2007, it even said that it is okay for a charity to rent facilities to a political candidate if the rental is on the same terms and conditions as the facilities are generally rented to the public.  In your case, it sounds as though you rented to the food business as you rented to others.  Your organization did not put up the political signs and, in fact, tried to get them taken down, but the business said it had a right to keep them posted under its lease.  Assuming that you didn’t reserve the right to control political signage in the lease, it seems pretty harsh to say that you should be tainted by an action you can’t control.

If you are really concerned about the image, you could put a no-political-activity clause in every new or renewed lease, but I don’t think you are required to do so.