Is it permissible for the wife of a deceased Mujahid to request the Mujahidin grant, knowing that her husband refused to take it during his lifetime, citing that his Jihad was for the sake of Allah?

There is no harm for your grandmother to take the veteran's grant if she is in need of it. The caliphs used to allocate grants to their subjects, especially to the Mujahideen and their families. Jurists have divided state grants into three types: grants for soldiers, grants for those in need, and grants for those performing public duties and functions. Evidence for the permissibility of seeking assistance from the state is found in what At-Tirmidhi and Abu Dawud narrated from the Prophet, peace and blessings be upon him: "Begging is a scratching by which a man scratches his face, except if a man asks a ruler, or for something that is absolutely necessary."