Question

Why does Mike go along with his grandmother when she doesn't recognize him the moustache

Answer 1

He went to visit his ill grandmother and she thought that he was her husband who is dead because her husband used to have a moustache. He states in this situation the necessity to don't have any regrets in love. This situation affected him so much that he decided to shaves his moustache when he arrived home.

Answer 2

Mike's grandmother confuses him with her dead husband, as they have the same name and they both wear moustaches. Mike goes along because he realizes how much pain her grandmother is enduring, she desperately needs to be forgiven for something she did. Mike tries to set her right but there is no point in it, he is scared of the consequences if she finds out the truth, and he realizes that his grandmother is a human being with a life, a story and some mistakes she has made. And he doesn't want her to have something to feel guilty about, as he does.