Sirius Black is half Grim.
In the 3rd book, Harry Potter sees a Grim near the Knight Bus! But it is really Sirius Black turned into a black dog.
But why does Sirius turn into a black dog?
Maybe it is because his surname is Black.
But Sirius in canine form, Grims are black dogs.
So maybe Sirius Black got Grim bloodlines.
But from where?
Maybe he got them from way back when the family started.
Or maybe there is a Grim side of his family that was either removed by the Black family for being a blood traitor or was never mentioned or seen.
But then why is most of his family human?
Maybe one or more members of his family had pet Grims!
Or maybe one or more members of his family had encounters with Grims.
Or maybe it is a coincidence.
UPDATE: I researched the Black family tree and I did not see any Grim bloodlines. But I did see Weasley bloodlines.......maybe Grim bloodlines were introduced by Weasley bloodlines!
SECOND UPDATE: I researched the Weasley family tree and I did not see any Grim bloodlines. But I did see Prewett bloodlines.