Mithrandir has studied the artifact that Ayorzén stole from the vault of Durthang and believes that if it might be cleansed of its corruption it could be empowered with a force for Good.
'I have studied the artifact that Ayorzén stole from the vault of Durthang. It bears a powerful corruption, but it was not made in the land of Mordor. It came from elsewhere, and the corruption that envelops it stems from its long stay in the Black Land. If this evil could be cleansed, I believe that Elrond could imbue it with a powerful and vital force for Good.
'Before that can happen, however, we must do something about the corruption that Mordor has worked upon it. There are different methods to accomplish this, though the Wise disagree upon the effectiveness of each. My preferred means for such a cure is to bring the corrupted item to the place where it was made, or to places of some significance upon its path, and to thereby diffuse the foul touch of Mordor that has, in the interim, claimed it. We must learn the story of this heirloom before it came to Mordor.'
The Wizard turns the artifact over in his hands, studying it for some clue to its origin. To your eye the heirloom is a small badge or medal, reminiscent of tokens worn by soldiers standing at their posts.
'There is a a slight depression here, ${PLAYER}, but it has been worn smooth by the passage of Time and the edges are difficult to discover. Even so, I can feel enough of the indentation to state with certainty that it was once in the shape of a star with five points.
'To my mind, that marks this badge as having once belonged to a guard of High King Elendil, perhaps at Annúminas, the seat of his power in the North. Bring it to that city, and see if you can cleanse the corruption that now encircles it. Techeron of the Dúnedain has returned to Annúminas to keep the peace there and may be able to help you.'
Techeron returned to Echad Garthadir in Annúminas following the War of the Ring.
Mithrandir believes that the corrupted badge came at first from Annúminas in the days of High King Elendil.
Techeron sent you to find the Steadfast Sisters in Annúminas, to see if they have seen any badges identical to the one that came out of Mordor.
Colm Fettering is a tomb-robber of some notoriety on the island of Rantost, in Lake Evendim, and may tell you more about the corrupted badge.
Techeron is at Echad Garthadir, in Annúminas.
Elrond is at the Haven of Orladion in Rivendell, north-west of the Last Homely House.
You have cleansed the corruption from the Badge of Ariant, and should bring it now to Elrond in Rivendell.