Temporary stair runner solution?

Q: I am renting a house with hardwood stairs. I have 2 large dogs and they are scratching them up. Is there anything I can put over the stairs without adhesive or anything else? I need something that is not permanent.

Floor runners? I do not want to nail anything since I am renting.

A: Perhaps an inexpensive stair carpet runner, held in place with rods secured to the riser by a screw eye hook at each end?