I had that same problem. I thought it must be Hüte, but I kept hearing an R sound that was throwing me off.
It shows that "Hute" is masculine, so then why does it have the female form of "the" which is "die"?
I think Duolingo sets me up to fail on these "write what you hear" exercises. I listen very closely several times and there is typically one word that isn't very clear. I write what I hear and it gets marked wrong. When I listen after getting it wrong the audio is perfectly clear and the word that I had to guess at is now obviously different from what it was before. It happens repeatedly, but I have experienced it only in German, not in Spanish.