Is expiation incumbent upon someone who swore an oath upon the Quran not to return to something, and then broke that oath, knowing that menstruation invalidates an oath made upon the Quran? And does an oath become binding by saying: "By Allah, I will not return to that," without mentioning the subject of the oath?

It is forbidden for a menstruating woman to touch the Mushaf (Qur'an) directly; she must use an interposer.

Expiation (kaffarah) becomes obligatory if what was sworn upon, or something that alludes to it, is mentioned. However, if it is not mentioned, then no expiation is due.

Swearing by placing one's hand on the Mushaf necessitates expiation if the oath is broken, even if the manner of swearing deviates from the Sunnah.