Speaking from personal experience, a cat bite is VERY hazardous, not only for anyone, but ESPECIALLY for the elderly.

I got bit by a cat back in November while visiting Kim in Lansing. I did not seek medical attention until 2 days later when the infection spread up my right arm (the cat clamped down on my right pinky finger and tore it open). The doctor in the ER told me if I had waited one more day, I would've been hospitalized. I should've had stitches but by then it was too late. The scar as really healed well and I was lucky that I got antibiotics for it.

Was the cat a feral or stray? Was the cat provoked? If the bite was non-provoking (meaning your grandma didn't do something to make the cat attack her) and the cat is someone's pet, you need to see if the cat's vaccinations are current (for rabies). I hope your grandma sought medical attention.