The Mark III extenders are designed for the Mk II 300, 400, 500 and 600 lenses to optimise focussing speed and be a match for their optics. If you look at at the MTFs on the Canon USA site for those lenses with extenders you will see they are exceptional. The-digital-picture site has crops for all Canon lenses with Mk II and III extenders on and you can see some improvement in CA for the x2 in particular. The IQ of the x2 III on the II series lenses is very acceptable, by repute and by my own experience on the f/2.8 300mm II.
5D IV, 5DS R, 7D II, EOS-M, Powershot G3 X, 400mm DO II, 300/2.8 II, 1.4xTC III, 2xTC III, EF 1.8 STM, EF 70-200/4 IS, EF 24-105, 15-85, 100-400 II, Sigma 10-20, Sigma 150-600mm C, EOS-M5 15-45, f/2 22, 11-22, Samyang 8mm f/2.8 fisheye