I get a "Solas approves" when I hand it in, which surprised me when I was first played through since it seemed over the top for a side quest that had nothing to do with him. I don't recall ever getting approval when you actually kill it though.
Ah, I edited my post but I guess it didn't go through. x_X I got the "Solas Approves" for handing it in, and I agree it is an unusually high approval considering the rest are "slightly approves" for helping actual people, but at the same time I'm not surprised that was one of the things that flew over most people's heads on a first playthrough.
I'm of two minds on this. On one hand, Solas is the older, wiser, and more powerful of the two. There's nothing wrong with Lavellan learning from him, and benefitting from his experience (IN THE BEDROOM AMIRITE). On the other hand, she needs to be able to stand for herself after he's gone. IMO for the relationship to ever be anything approaching healthy, his strength needs to complement hers and help her grow, rather than becoming a crutch for her. This is especially true for muggle!Lavellan, who has no magical training and is likely more dependent on his expertise at the start.
I think most of us can definitely agree to this, and I think it's what makes me cringe on fics/pics where Solas and Lavellan refer to one another as hahren/da'len constantly. It puts them on uneven footing, which is definitely how it is at the start (and thus appropriate for the game to use it), but afterwards - and especially once they're officially in a relationship - it becomes inappropriate (IMO anyway, I can see why others might disagree).
Lavellan is the Inquisitor afterall, she's a leader! Ain' no one her hahren! I headcanon my girl calls Solas hahren only once seriously, to follow canon, but any other time she uses it when being sarcastic with him. My Lavellan is a sassy little ****. x)
Also I love the phrase muggle!Lavellan, thank you for that. xD
Oh man, I completely forgot about that! My headcanon (and playthrough) has her clan in Wycome as part of the council. I dread to think what would happen if she showed up with no vallaslin...
"Da'len, what happened to your face?"
"I don't know! I just woke up like this!" *shifty eyes*
My girl's got it all worked out. "So I fell out of the Fade, with this mark on my hand *lets it sizzle* and my Vallaslin was just gone! Even the embarrassing one that jerk did on my butt for a bet!" Okay so the last bit may not have happened. She can say what she likes, no one from her clan comes to see her!
I may have watched and/or overanalyzed all of this entirely too much.
Excuse you, little comment, there's no such thing as over-analyzing anything. 
I took pity on poor man and went Cullen route. I respect his privacy. Kind of.
I always give him the evidence I find. I'd feel bad for going around his back, but I might do it this time around to see the War table mission. 