"My grandmother lives in that village."
Good example of a translation may be correct in meaning but miss the subtle difference what the focus is I answered 私の祖母はその村に住んでいます But the japanese solution the focus is more like "that village is where my grandmother lives" Duo japanese fails without this important context
You're not wrong, per se. Here is an example where your answer works:
You've used が because you were answering my question. In Duolingo's answer, they've used は because they are starting the conversation, rather than answering my question.
If there was no で、the given choice of words was defective. In addition, 私の祖母はその村に住んでいますanswers the question "Where does your grandmother live?" In contrast, その村には私の祖母が住んでいますanswers the question "Who (if any, among those you know, ) lives in that village?" or "Does anyone you know live in that village?" It'd be more natural to presuppose the question "Where does your grandmother live?" Yukio Kachi