midrash - What did women have to do with the moon's shrinking?

In the Mishna Berurah (426:1) it says (with loose translation):

ונשים פטורות מלקדש הלבנה דהוי מ"ע שהזמן גרמא ואף דכל מ"ע שהזמן גרמא נוהגות הנשים שמקיימות ומברכות עליהן מ"מ מצוה זו אין צריכין לקיימה משום דהם גרמו פגם הלבנה

Women are exempt from "sanctifying" the moon as it is a Positive Commandment which is "caused" by time. And even though women are accustomed to do all such Mitzvos either way, and say a Bracha when doing them, they do not need to do this Mitzvah because they caused the "defect" of the moon.

I assume that when the Mishnah Berurah says "defect" of the moon, he's referring to the story of the moon originally being the same "size" as the sun and shrinking (see How did the moon shrink?). Please correct me if this premise is wrong, and there was a different incident with the moon.

If so, what did women have to do with that story? Women weren't even created yet...

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Note: I see that the משנה ברורה and מגן אברהם that mention this are quoting a של״ה. However, I have no idea where to look for it, so I would appreciate if anyone would point me in the right direction…