Tip: for instant quest completion as a Trevelyan pick the special noble option. (I don't recommend killing the guy, although D's response is humorous, if displeased.) I actually think that the noble is the best option here. Granted the "do you know who I am?" schtick is groan-worthy, but it yields the best results. Dorian only slightly disapproves because you're going against his wishes in interfering, you get the amulet immediately, and you don't let this POS get rewarded for bad behavior, which is what happens if you agree to the terms.
Meh, I don't like playing human nobles at the best of times. Just calI me Sera. I like human noble characters as companions, friends and love interests, but I don't want to play as them myself.
To be honest though, I'm playing my male Lavellan as being much more mellow and forgiving than my female Lavellan. She'd kill anyone that looked at her friends cross-eyed. He's willing to give second chances or swallow his pride to help people he doesn't like if it means helping his friends. I mean, he's already recruited the Sword Coast bandit leader that killed his men, let the fake compte you have lunch alongside Josephine with go, elevated the family that wanted her dead up to nobility so they would call off the contract, and let the noble in Sera's personal quest walk away (although he regretted it soon after; when Sera bawled him out back at the tavern, he instantly agreed it wasn't the best choice).
Given my male Lavellan's track record, he's willing to swallow a little pride and help a weasel get into the nobility if it means getting his beloved's amulet back. I kind of see my Lavellan as the kind of guy that'll buy an overpriced painting, knowing he's being ripped off, because he knows it'll make his beloved happy.