Is it permissible to pay Zakat to a sick grandmother who is in need of treatment, given that she has two sons with low incomes that are insufficient to cover the costs of treatment except through usurious borrowing, and is it necessary to inform them that the money is from Zakat?

The basic principle is that it is not permissible to give zakat to one's ascendants (parents, grandparents) or descendants (children, grandchildren) because one is obligated to spend on them what suffices them from begging people. This is subject to two conditions: that the ascendant or descendant is poor and unable to earn a living, and that what is spent is surplus to the giver's own needs and the needs of those whose maintenance is obligatory upon him.

However, it is permissible to give zakat to ascendants and descendants if they are poor and the zakat-giver is unable to spend on them.