Often nothing. The majority of the shots Kyle took were 200 to 400 yards - not the 1000 yard shots we usually associate with the term "sniper" (although Kyle made his share of those too). A 200-400 yard shot is very typical of the shots taken by skilled rifelman in open battle and certain don't require anything more good, properly adjusted, iron sights. I have known several ex Nan era military vets who could shoot accurately at 500 yards with an M1 or Remington 700 using nothing but iron aperture sights.
I was watching a show on AHC last night that was talking about the M1 Garand that said 400 yard head shots were common among skilled infantrymen.