"Excuse my grandfather, he is old."
Translation:Scusate il nonno, è vecchio.
The determinative article is not used with the possessive before a singular family member: vediamo mia madre/we see my mother, mangia con suo padre/he eats with his father, mia sorella legge un libro/my sister reads a book
The determinative article is used with the possessive before multiple family members, or when the possessive is loro: i miei fratelli scrivono/my brothers write, le tue cugine cucinano/your cousins cook, la loro figlia mangia una mela/their daughter eats an apple
But if the possessive is not present, then it can be translated literally in English to the grandfather. The difference is that in Italian forgoing the possessive and using only the article would be fine since the group you're speaking with probably knows whose grandfather is whose.