Actors often have a lot of say over their own costumes, makeup, and hair styling. Even supporting guest cast on a TV series are generally given some choices in the wardrobe department.
As a first-tier supporting actor in a film, and someone they weren't about to get rid of, Walter could have asserted himself and said "This doesn't look good to me." Instead, he obviously took a passive approach, whether through timidity or laziness. That is why he ended up in the foppish, "Buster Brown" collar in Star Trek III. That and Leonard Nimoy either not caring what Chekov looked like, or having taste as bad as the costume designer (meaning pretty bad; even Shatner's civilian suit looks terrible, and none of the civvies in the film look cool at all).
From what I read, when Koenig's ridiculously high collar showed up in the dailies, a studio executive ordered them to get rid of it. So it disappears from the rest of his scenes.