Why is “saya menyewakan mereka rumah itu” not correct ? Is it not similar to a previous test sentence “ Who taught you this” where “siapa yang mengajarkan kamu ini “ instead of “siapa yang mengajarkan ini kepadamu” was accepted by DuoLingo?
No, that would have a different meaning.
That would mean that you are renting out that house "for them", "on their behalf".
That would make "they"/"them" the owner (not the renter) of the house.