"Tu" = The, That
"Tuto" (and "Tuhle") = This
Trying on my own (covering the suggestions), I got "Tuto ženu neznáme". Does Duo accept this?
Yes, that's fine.
"Tutu zenu nezname"
Isn't that the same?
It should be either "tuto," as shown above, or "tuhle." (I don't think "tutu" is a word, but if it is, a native speaker may correct me.)
I answered "Neznáme této žen" and it got accepted but the best translation provided doesn't really match my answer. Why is it accepted?
"Neznáme této žen" is not accepted. Either an error happened or the answer was different.
I think an error occurred then, quite sure what I entered.