I don't know what it means for a house to have a hatchment.

I've only ever seen them in churches. Many churches have one from about 1800, 1820 with the royal coat of arms. Only in a few cases do you see a real heraldic hatchment as a memorial to someone deceased. Usually these are on the north or south wall, whereas the royal arms are on the west wall under the bell tower.

They're quite large. The background is black. The arms are painted upon it.