Maybe purists would prefer ο διάδρομος (lit. through the house)? η παστάς (corridor)? One ancient Gk lexeme was δίοδος (thoroughfare, durchgang), but it was a word for the way through anything. The question for me regarding English loanwords is: Why is DL introducing us to this word? Is it the most common way to say hall / hallway? Are there other options? Since Greeks have always had homes, even taking into consideration that architecture changes with time, there are options in Gk for hall. It would be helpful if a native Gk speaker chimed in on this word and on loanwords. After writing this par. I noticed that modern Gk moderators comment on this topic here: https://forum.duolingo.com/comment/18053460 Apparently προθάλαμος and διάδρομος are options. The former means more or less "in front of the inner chamber" (θάλαμος was an inner room) while the latter means "running through" i.e., passageway.
Χολ is used in greek to describe the room that you enter when entering the house. Διάδρομος is the hall in the meaning of a room that's a passageway to other rooms (you don't stay there, you usually just walk it to get from room to room). Προθάλαμος is mostly used for lobbies. Παστάδα (παστάς is the ancient spelling) is an old word not used much and in modern greek means "newlyweds' chamber".