He arrived very late, but it didn’t mind; I just wanted to see him.
He arrived very late, but I didn’t mind; I just wanted to see him.
Mind means to feel annoyed or unhappy about something. The subject is the person who has this feeling: ‘There is some noise, but I don’t mind.’
Matter means to be important. We often use it as its subject: ‘There is some noise, but it doesn’t matter.’
Compare: ‘I don’t mind.’ ‘It doesn’t matter.’