Your choice...
 

HTBT but I think I would have conceded the buck to the kid.

Never miss an opportunity to teach when in a 'teachable moment'.

Seeing generosity and compassion is an important lesson for a young person especially in 'our world' (the scope of hunting and hunters).

That youngster will forever remember this lesson. I'll bet his Father will carry this story to every camp, trip and excursion he goes to as well.

I don't. There is no need to if you skin and quarter your deer soon after you kill it. I can skin and quarter my deer without ever touching the guts. That includes getting the inner tender loins. It's not that difficult. As for the op's question, it is your deer, but you did a good thing. If you hadn't shot the buck, they probably would have never found it. Good deeds get rewarded.

I like to think I'd have let the kid have the deer. You've got serious good karma comin' your way, ERM!

I'm a logger so i'm in the woods all the time, and find wasted deer frequently, due to poor shooting or poor tracking. I'm glad u put the suffering buck down, I'm also glad the father was tracking the deer. Don't know what i would've done could've went either way.

It sounds like they had a good attitude, i'm sure that helped there case, in making your decision.

I'm a logger so i'm in the woods all the time, and find wasted deer frequently, due to poor shooting or poor tracking. I'm glad u put the suffering buck down, I'm also glad the father was tracking the deer. Don't know what i would've done could've went either way.

Why do I go to post and it says i'm not logged in even though i was? I'm sorry about the double post. The other day i logged in and made a long thought out post entered it and it said i wasn't logged in, the post never made it? by then i lost my thought lol.

I can relate
 

I just stumbled on to this sight and your post. It brought back some
memories. Ten years ago, or there abouts, on the second day of the season, I
listened to the shooting coming from the East. The shooting would hault, and then
someone would open up again. I wish I had counted the shots because there were way
too many for this to continue. But what I was sure was a buck was still going, and
the shots were getting close to my area. Then things got quiet. About 10 minutes
had passed when I saw him coming my way, waited for the shot, and dropped him.

I took a look at the deer, one gut shot, and went back to my stand in case
something else mightbe moving, 'cause I knew the B.I.L. hadn't shot. Fifteen
minutes later I figured it was time to tag and dress. When I started to work on
the deer, a guy saw what I was doing, and came running, along with his thirteen
year old son. The father was like a used car salesman on crack. He spit out lie
after lie why this was the kids deer. The kid was as stiff as a board, and shaking
like a leaf. I felt sorry for the kid. He might be loosing his first deer, and,
he was taking in all the crap his father was dishing. It was a deer. It was not
worth getting nuts over, and pa was nuts. I said that they could take the deer,
and headed up the ridge to the brother in law's stand, and told him the story.

He wanted to see the buck, so I led the way back. When we got there, the father
was sitting on the deer, like it was a horse, holding the rack up, saying he had
never seen a bigger deer in this area. Okay. I had gotten bigger bucks, but I had
really worked for them. This is a easy come, easy go. Every deer is a gift. You
are free to do as you wish with your gift. I hope we both made the correct
decision. We did not make the situation worse, and you have to feel good for
taking the high road, even though it might not feel like it right now.

A couple things stand out. You didn't hear their shot....or at least didn't mention that on here. So they were tracking it...perhaps for a distance. That means they were doing the right thing to try to locate that animal. Second you followed your instinct. You did the right thing by you and by the kid. From the wound you describe, it could have been a quartering away shot where they had reasonable expectation that the bullet would take out a lung. I have seen a couple folks say don't give the deer over because it will somehow teach a lesson to make a better shot. Maybe. But more likely it would be a memory for the kid of making a shot and tracking a deer and having someone else take it out of the woods.
The way you left it, there is much greater potential for positive lesson learned from the experience. I'd like to think I would have done the same thing.