Arun said "This girl is the wife of the grandson of my mother". Who is Arun to the girl?

Father-in-law

Arun said 'this girl is the wife of the grandson of my mother".

"grandson of my mother" means he can be son of Arun, "this girl is the wife of the grandson of my mother" means girl is wife of Arun's son.

Arun can be Father in law or Mother in law as the gender is not determined but when we go through the option Mother in law is not in the option so Father in law is the possible answer. 

Hence, Arun is Father in law of girl.