This may have been asked before (so i apologise in advance), but i did go through all 6 pages in this thread and found no mention of the following:
I was a bit surprised at how they shot OJ's wife like no big deal, supposedly killing her, but they would not just simply put a bullet between OJ's eyes. Did they timetravel the wife's dead body back to some looper so to make it disappear? Couldn't they have done the same with OJ, thus not allowing the chance of his loop run? I have yet to see a dead body run.
Killing OJs wife was an accident. Murder is a big no-no, and killing someone is going to leave some sort of trace. The cleanest thing to do is send them back first, then kill them, so there's no blood, body, weapon, anything in the future. The gat men heard a sound, and some kind with an itchy trigger finger shot her by mistake. They then did there best to cover up the evidence (by torching the house). Whether they send her body back, too, or just burned it is never explained.
So I don't think killing her was "no big deal", and it's still cleaner/easier to send the person back first.
Could not have said it better myself.