I usually think of that sound as being represented by "zs," and the specific reason is because of the actress Zsa Zsa Gabor (I believe the Gabors were Hungarian, if I'm not mistaken?).
This isn't very well put together, because when you run your mouse over it it says 'ze' at the end, but then fails you and tells you that the end sould be only a z and no e -.-
OK, I think I know what happened. Generally, the basic word is "zwierzę". This option is the best one and definitely should be accepted. But sometimes there is some bug and the correct option is rejected.
Now, there is a word "zwierz" in Polish. It's not that neutral, and personally I wouldn't accept it. But this exercise is shared with "English for Polish speakers" course and they accept it. So it's also among the accepted answers for us.