In the 2011 anime version of Hunter x Hunter, Gon never speaks to his grandmother. I have rewatched episode 1, 37, and 38, but he never addressed her. We don't see him telling her goodbye or hugging her either. Nor is Killua shown to acknowledge her.
Gon's body language in 37 and 38 seems to pay attention to her when she speaks, though. And in the non-canon re-hash episodes 13 and 26, his letters begin, "Dear Mito-san and Grandma,". Countering these instances, at time-mark 9:25 of episode 37, Gon converses with Killua and states, "Since Mito-san raised me by herself". Although in episode 1 of the 1999 version, we do see both Gon and Kite speak to her.
Until I found the instances of acknowledgement, I was beginning to wonder if by the time he turned 12 his grandmother had become a ghost that only Mito saw. It seems clear that Gon sees her, too, though. But alive or a ghost, why does he never speak to her? I guess it is possible that it is abnormal in Gon's culture to speak to a grandmother when your parent (figure) is there. At 14:57 of ep.1(1999), the point Gon speaks to her, they are alone in the kitchen, with Gon asking, "Where is Aunt Mito?". Once Mito shows up, he doesn't speak with his Grandmother again. (This is the scene where Mito brings Gon his father's fishing rod.)
The simplest explanation is that the animators and/or Togashi simply had nothing for Gon to say to his grandmother. Still, it seems at best awkward that he tells Killua that Mito raised him by herself, and that, during his extended goodbye to Mito before leaving for the exam, he ignores his grandmother.