Do landing gear doors need repairs after a gear gravity deploy landing?
No, they do not get damaged.

The Main Landing Gear (MLG) or Gear Bay doors can and are regularly opened on ground for maintenance purposes. Even with fully compressed oleos the MLG doors are still off the runway surface. Have a look at this Air Canada A320. You can clearly see the doors being well above the bottom of the MLG.

If you came to your conclusion by watching the white puff of smoke coming from the area of the open MLG doors - that's actually the burning rubber from the nose gear touching down.