I wrote "Ke hale," and it was accepted. Since this is teaching the articles, it should not be this lenient. My answer should not have been accepted. I also noticed that "Ke" was listed as one of the options in the hover menu. It should not be listed here. Ka should be the only option in this case.
Duolingo allows single letter "typos", but there is a way to specify that "ka" and "ke" should not be accepted for each other, so hopefully they'll fix that.
On the other hand, the Hints (what you are calling the hover menu) cannot be specified per exercise and will always show more than just the answer which is correct for the current exercise.