We have a tile at the entrance door to the common stairwell that has
been damaged by repeated contact with the hook used to hold the door
open. It is a semi-circular abrasion of the glaze. The tile survived
for 100 years until new neighbours moved in but that's another story.

I'm wondering the best way to carry out a repair for maximum
durability. Ordinary filler or enamel paint would just wear away.