Sirius has Remus apparate them to Hope’s place first; he doesn’t want to go home to that cold empty flat just yet—doesn’t know if he ever wants to go back. Remus, although he’s spent the past few meetings hedging and making polite refusals and generally keeping Sirius as far from his mother and home as he can, takes one look at Sirius and invites him in instead of the cold dismissal Sirius had been steeling himself for.