Purity is a Radiant Quest in The Elder Scrolls V: Skyrim.
To trigger this quest you must have at least completed a Radiant Quest for either Vilkas or Farkas. Having done that, they will present the option to talk about a more personal quest.
You should have at least 1 Glenmoril Witch Head in your inventory before completing any additional Radiant Quests for either of the brothers.
Locations[edit]
Quest Giver | Location |
Vilkas | Whiterun - Jorrvaskr |
Farkas | Whiterun - Jorrvaskr |
Walkthrough[edit]
Having helped out Vilkas/Farkas at least once, talk with them again. There will be a dialogue option to help them with a more personal matter. They will also mention being distracted by such thoughts. if you do not have any more Glenmoril Witch Heads, you will be directed back to the Glenmoril Coven to collect one. Once you have, you will want to head back to Ysgramor's Tomb. If you have cleared the area, you can use the shortcut back to the final chamber to quickly reach the Flame of the Harbinger.
Approach the flame and interact with it to throw the Witch Head in. This will call out either Farkas's Wolf Spirit or Vilkas's Wolf Spirit depending on who is with you.
Defeat the spirit and the Companion will be cleared of their Wolf Blood.