"Binky's grandmother" is not an official name.
Binky's grandmother
Binky's grandmother
Gender Female
Animal Bulldog
Residence Binky's grandparents' house
Family Binky's grandfather (husband)
Mr. Barnes (son or son-in-law)
Mrs. Barnes (daughter or daughter-in-law)
Binky Barnes (grandson)
Mei Lin Barnes (adopted granddaughter)
Shelley Barnes (possibly father-in-law)
Other relatives (seen in Postcards From Binky)
Cartoon debut "Postcards from Binky"

Binky's grandmother (possibly Grandma Barnes) is the grandmother of Binky Barnes. Binky taped a video postcard for his grandparents because he never really gets to see them a lot because they live far away.