Is it permissible for a woman to observe Iʿtikāf on behalf of her deceased parents?

The summary of the fatwa (definition) is that the deceased benefits from the living through what is supported by evidence, such as supplication for them, seeking forgiveness, giving charity on their behalf, performing Hajj and Umrah (definition) for them, and settling their debts. Some scholars have gone to the extent of permitting the dedication of the reward of any act of worship performed by a Muslim to a living or deceased Muslim. The correct view is to restrict it to what is supported by evidence. As for parents, Islamic law has made the child part of the father's earnings, based on the Almighty's saying: "And that man will not have but what he endeavored for," and the Prophet’s (peace be upon him) saying: "Indeed, the best of what a man eats is from his own earning, and his child is from his earning." So, whatever righteous deeds the righteous child performs, their parents receive a reward equal to theirs, without anything being diminished from their own reward.

Regarding women's i'tikaf (seclusion in the mosque), it is conditional upon the permission of her family or husband, and that her i'tikaf does not involve any fitna (temptation or discord).