Saku's grandmother is a genuinely kind-hearted woman who's become her primary guardian. The two have a really close relationship—Saku actually chose to stay behind in Japan rather than move overseas with her parents, mainly because she couldn't bear the thought of her grandmother living alone. It's clear how much they mean to each other.
Interestingly, Saku inherited her petite frame and general appearance from her grandmother. There's even a flashback in the manga showing what Mitsu looked like at 15, and you can definitely see the family resemblance.
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