It might depend on the aircraft type and towbar - I'm sure many of you have seen, either in person or video, a tug hooked up to a 747 and the tug is under the nose of the plane.

The most likely parts to suffer damage on many planes would be the radome (since it's the part furthest forward made of composite material) and rubber hydraulic lines around the nose gear.

I would expect that contract maintenance, or at least the crew, inspected for damage.

Jim