When I came across Narzulbur, the Orcs there asked me to retrieve some gloves for them from Stony Creek Cave in order to become blood-kin and enter their fortress. I did so, and while clearing out the cave I also came across Finn's Lute. When I tried to put it in a dresser in my house for storage, the game told me I couldn't because it's a quest item.
After searching online I found that it is required to finish a quest given by Inge Six Fingers, in the Bard's College in Solitude. I've already finished the quest to gain entry to the Bard's College, so I went there and talked to her. She gave me the quest reward (quite a few skill increases), however the lute is still in my inventory (probably because I didn't have the quest before getting it).
So how can I get rid of Finn's Lute from my inventory, since the game won't let me drop it due to it being a quest item?
I tried talking to her multiple times, but each time she acts like I finished the quest (I only got the skill increases the first time, though).