Who is Grandma Schmidt from Extremely Loud and Incredibly Close and what is their importance?

One of the novel's secondary narrators, Oskar Schell's paternal grandmother is early on portrayed as slightly senile and smotheringly touchy. She knits white mittens and scarves for Oskar, gives him a subscription to National Geographic and his Grandpa's abandoned camera. She lives under her maiden name on the third floor of the building across the street from Oscar and his widowed Mom, a lawyer who often works Saturdays and Sundays. As a result, Grandma has taken care of Oskar since early childhood and is his closest confidant since his Dad's death.