When Harry first met Kreacher, he was muttering under his breath but that was a very audible muttering.
oh, my poor mistress, if she knew, if she knew the scum they've let into her house, what would she say to old Kreacher, oh, the shame of it, Mudbloods and werewolves and traitors and thieves, poor old Kreacher, what can he do....'
Harry Potter and the Order of the Phoenix, Chapter 6 - The Noble and Most Ancient House of Black
then he said to Hermione
'The Mudblood is talking to Kreacher as though she is my friend, if Kreacher's mistress saw him in such company, oh, what would she say--'
However, Kreacher was present at the headquarters of the order, but things like Lupin being a werewolf were only discussed in meetings. So how did he found that out? Moreover, Hermione being a muggle-born was not even a subject to come around as most of the order people don't know her and those who knew her don't care less to mention it. So how was Kreacher getting the information for his muttering?