Taeron returns to Elrond - thanking him for the assistance. He shows him the newly forged axe and spends as much time with the smiths as he (the smith) can afford. He describes him the travel and gives him best wishes from Grandir, the dwarven master smith.
As they talk, Taeron helps him with whatever heavy lifting he requires. He hauls coal or ore from one place to another - and works with the smith as best as he can, not to feel as much like a burden.
In the evening, he promises the smith to bring Valtore with him during his next visit, so that the dwarf can share his new found knowledge of the metal.