From Memory Alpha:
According to Fontana, the pink coloration of the Kzinti uniforms and ship in the episode was a result of Director Hal Sutherland being color blind, and thus unable to discern them as anything but shades of gray. [3] However, storyboard artist/character designer Bob Kline laid the blame on color director Irvin Kaplan. "Pink equals Irv Kaplan," shared Kline... "Irv was in charge of ink and paint, coloring the various characters and props (and he would do it himself in his office, he would sit down with a cel and paint it). He was also referred to by many people there as the purple and green guy. You'll see it in a lot of scenes, purple and green used together – that was one of his preferences. He made dragons red, the Kzintis' costumes pink. It was all Irv Kaplan's call. He wasn't listening to anyone else when he picked colors or anything."