Are you sure? The word sounds distinctly Turkish to my Greek ears [1].
It's funny but there's long-standing confusion between me and a friend regarding what a "musmulo" (singular) is. I know by that name a small, round, orange-yellow fruit with soft, tangy flesh and large-ish but very smooth stones - known in English as a loquat. I'm from Athens, but my friend who is from Corfu knows two things as musmula: the loquat and the medlar fruit.
I notice also in sister threads that there is some linguistic confusion about medlars and loquats in other places, e.g. two French users discuss whether "néflier" is the loquat or the medlar fruit, in French.
This year I was at my Corfiot friend's house in winter and they have medlar trees in their garden, so I had the opportunity to watch the bletting process in action, as it were. Basically my friend and my friend's dad picked a bunch of medlar fruit and put them in wicker baskets wrapped in newspaper. Then a few weeks later they ate some. To be honest, I didn't try them, because they looked and smelled ... rotten? I guess? My friend ate a few but some had actually gone bad and had to be chucked out. Strange fruit, really.
There are Modern Greek words that came into Greek from Turkish, but where the Turkish word comes from an Indo-European root (though it's not always clear if that is Greek or Persian).
Examples include karpouzi (watermelon, from Turkish karpuz, from either Persian xarbuz, "melon", or Greek karpos, "fruit").