We don't know a whole lot about Grandpa, but he plays a super important role in the story anyway. Here's how: He starts off the family story with his "great hunger" (1.3) in Chapter 1, which gets the whole Haji bandwagon on the road. This means he's a very hard worker, which is something that he definitely passes onto his son and grandson.
Hassan describes him as "a dour fellow" (1.6). The grandkids aren't able to get a lot of information out of him about his life story, though he's also described as "a good provider" (1.7). Part of this is that he's a little bit of a miser, hoarding the money he makes by burying it in a hidden location. Hey—it guarantees there's some cash on hand when you need it.
Bapaji manages to get through the political turmoil in Old Bombay when many of his countrymen are fleeing for their lives; he's also pretty much a peasant who can't read or write, but has a good knowledge of the land and how to make a living with his own two hands. So by the time that Hassan is around, he has become "a man of respect in the shantytown" (2.69) because of his hard work and determination. Yup, this guy's a survivor.