How do I get rid of Finn's Lute?
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.