What is the ruling on a woman who performed Umrah while she was menstruating, believing herself to be pure, and then discovered her impurity after performing Umrah? Is she required to perform another Umrah, given the difficulty of doing so?

If a woman discovers that she performed 'Umrah while impure due to menstruation, her 'Umrah is invalid according to the majority of scholars, as they stipulate purity for circumambulation (Tawaf). Therefore, she must refrain from the prohibitions of ihram and return to Makkah to perform a valid Tawaf, then Sa'y, then Taqseer (shortening of hair), and with this, she will be released from ihram. As for the prohibitions she committed out of ignorance: for those that involved causing damage, such as cutting hair or clipping nails, there is a single fidyah for each category (a sheep, or fasting for three days, or feeding six needy persons). For those committed for mere indulgence, there is nothing. If intercourse occurred out of ignorance, it does not invalidate the 'Umrah. The Hanafis and a narration from the Hanbalis do not stipulate purity for Tawaf. In this case, the Tawaf would be valid, and she would owe a damm (a sheep), and she can appoint someone to slaughter it in Makkah and distribute it among the poor of the Haram.