In English would you say "the cat washed nothing yesterday"? You could but you would probably say "the cat didn't wash anything yesterday". As you continue studying you'll learn that the word nada can be used this way, it makes no sense to those of us who speak English as a first language so we just have to learn it.
That's because "nada" means "nothing", so "el gato no lavó nada" is "the cat didn't wash anything" (or "the cat washed nothing"--Spanish uses double negatives, but English can't), just as "el gato lavó todo" would be "the cat washed everything".
I'm not a native Spanish speaker, but it looks like "at all" is "en absoluto", so I think "the cat didn't wash at all" would be "el gato no se lavó en absoluto". In that sense, it sounds like we're talking about the cat washing himself, so I used lavarse rather than just lavar.
Because Duolingo has to choose one correct answer (usually out of many possibilities) to display for the sentence, and the word bank has to contain tiles that allow you to form this answer.
For this exercise, the primary correct answer (the one displayed at the top of this page) is "The cat didn't wash anything yesterday", so the word bank contains the tiles necessary to form that sentence. The sentence one can form from the word bank should be the same as the correct answer Duolingo has chosen to display for a given exercise.
And tell me how that would make a difference between using the word "not" instead of using "n't"? Let me spell it out a little more clearly for you. The contraction "didn't" as 2 word blocks put together has the same exact meaning as "did" and "not" put together in 2 sequential word blocks. They are both grammatically correct. The contraction spelled out with the apostrophe replace by the character "o" is "didnot" .
I think we all understand the difference between "did not" and "didn't." But here's the thing: Most questions have several acceptable answers. Some have literally hundreds. It would take up too much space (and programming time) to display them all. So, Duo shows us only one of the many options. And, as sassfb points out, "the sentence one can form from the word bank should be the same as the correct answer Duo has chosen to display for the current exercise."
So the question remains: Why would Duo want to use an English contraction in the first place? Perhaps Duo wants to remind us that English often uses contractions when Spanish does not.
If you find the word tiles annoying, you might prefer typing your own answers from scratch.