No one would say hainele sunt bătrâne. Instead vechi is more appropriate. The former is more about being old as a person.
I think, it is correct ”the grandparents' clothes..."
Is grandparent plural or singular here? Plural possessive would be grandparents'. If it is NOT meant to be plural, then perhaps "grandfather's" should be accepted as an alternate answer.
bunicilor is genitive plural, so grandparents'