Looking back at this chapter, I think there was some things lost in translation regarding the grandfather. I'm assuming that the words he was using were a bit different than the traditional term grandfather, or at least he was using terms she wasn't entirely familiar with, and the terms were different enough that she didn't initially understand who he was until he said "I'm your dad's dad." It's probably similar to how the term "uncle" in Japanese, Oji-san, can also refer to some older man that one is not familiar with.