Do runways need to be repaired after gear up landings?
Runways are usually made of several feet of reinforced concrete. Any damage to them after a wheels-up landing is superficial at best. Details depend on circumstances, but in general light aircraft will cause less damage. A full wheels-up landing is rather easy on the runway: The aircraft's fuselage and wing fairing structure are flexible and malleable, so it will buckle and bend until the local surface pressure is too low to cause more bending. To really damage a concrete surface you would need carbide tools, not sheet aluminum.

An unwheeled landing gear strut of an airliner is probably the worst scenario. The Airbus in the linked video had only a damaged nose gear, which carries a small fraction of the total load, and you will see in the close-up at the end of the video that the runway did not suffer. A similarly damaged main gear, however, will cut a groove. 

All what is needed for repair is some fast-curing liquid for filling the nicks and scratches and some paint to repair the runway markings.

If you land a composite aircraft wheels-up, the concrete will act like sandpaper on the structure. The landing zone will be marked by white epoxy dust. A broom is all what is needed to put the strip back to its initial condition.