The correct option is A nostalgic
Option A: 'Nostalgic' means 'someone who shows a yearning for the past'. It is relevant to the given statement, as the grandparents showed their yearning, desire for their past, when they were present with a picture of their wedding.
Nostalgia is a remembrance of the past, with a feeling or a wish that the past could be re-lived again.
Hence option A is correct.
Option B: 'Petrified' means 'frightened or terrified'. It is a reaction to something unpleasant. The grandparents' wedding does not indicate an unpleasant thing.
Option C: 'Extrinsic' means 'external or alien'. The meaning isn't relevant to the statement.
Option D: 'Disparate' means 'contrasting or different'. This word does not complete the sentence in meaning.
Hence options B, C and D are incorrect.