Supposedly, they have 100% perfect tracking and biomonitering implants in the future. If you kill someone the police will know exactly when they died and who was there with them. That means that the identity of the killer will be pretty obvious.
Sending them back in time means that they vanish from the tracking system, but there is no death signal.
But they'd know where it was, when it was, and who was nearby when it happened. Then all it takes is finding evidence that a single one of these mysterious disappearances were killed in the relatively recent past (which they were, hence older versions being sent back to be killed by their younger selves)... argh, nevermind. I give up trying to figure out how to rationalize crummy plot elements like this.
Yes, yes, I know it's really just a prop for the movie. This just doesn't make a lick of sense. Doubly so if the time travel technology itself isn't easily portable (hence the signal disappearing wouldn't give its location away).
EDIT: Oh, someone else ranted about it, too. Sorry. I really need to finish reading a thread before replying.