How do I get rid of Finn's Lute?

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).

This is a known bug

[PS3][XBox][PC] Finn's Lute may get stuck in your inventory, not allowing you to sell the item or drop it. Pickpocketing Finn's Lute after completing the quest will also make it permanently part of the player inventory. PC players can use the console command player.removeitem 000DABAB 1 to remove it. Console players are effectively stuck with it forever.

I talked to her and got my skill perks. After figuring out it was glitched, I used sneak at night and killed her. The quest then was marked as failed and cleared my quest que, even though I got the reward for it. I dropped the stupid lute from my inventory right next to her body.