I dunno, I did it because it was part of the main quest? I wasn't even paying attention to the details. I just wanted to completed a few main quests. I didn't know that you had the oprion to not do it if you wanted to progress further in the civil war conflict.
How is that part of the main quest? o.0 You don't even have to talk to that stupid Thalmor in Markarth. I just talked to him to see if I can rile him up, so he would fight me, before I knew it, I had agreed to that quest. I did break into the guys house, took the amulet, but then realized I would never get rid of it, since I would never turn that guy into that stupid Thalmor, so I just re-loaded a prior save. Then, once we took the Reach, the quest failed and I was happy! hahahaha