Old World Context: This saying overlays a common task with a spiritual meaning. The cultural setting requires houses with doors; the social expectation is that the householder will answer a knock at the door. Jesus taught the people to pray, addressing God as Father. He is therefore a close relative who will receive us if we approach him properly. Jesus assures us that God will welcome us; he will not inhospitably ignore our knocking (prayers).
Book of Mormon Context: Mormon does not record how the Nephites announced themselves to those inside a house, but Mesoamerican dwellings had no wooden doors. Doorways were (and traditional-style homes still are) typically hung with fabric. Thus, they must have substituted some other gesture for knocking, although obviously the image of God as a father graciously receiving his children would have been quite appropriate.
Comparison: There are no changes from the Matthean text.