Is it obligatory to repay Zakat if it becomes apparent that its recipient – who appeared to be poor – is from the Prophet's household (Ahl al-Bayt)?

It is not permissible to give Zakat to the Ahl al-Bayt (the Prophet's household). However, if someone paid their Zakat to an individual after investigation, believing them to be deserving, and it later became clear that they were not, then the Zakat is considered valid and the person is not required to pay it again. This is the view of Abu Hanifa and Muhammad, and it has been chosen by some contemporary scholars, based on the Almighty's saying: (So fear Allah as much as you are able) [Quran 64:16], and the noble hadith: "You will have what you intended, O Yazid."