2. It was the first time the narrator had met Laura's grandmother.

Solution:

The narrator says, 'Though we were not very close friends, I decided to drop into her house on my way home.' Upon arriving, 'A slim, elderly lady in a jumper and sports trousers opened the door. I explained to her who I was and she smiled warmly.' This implies the narrator had not met her before. The narrator then states, 'The lady who let me into the house was Laura's grandmother.' This confirms it was the first meeting.

Answer: 1) True