Does attaching part of a door to the wall of a shrine qualify as assisting in the construction of the shrine, and what is the ruling on that?

What the father did by building a wall next to the tomb's wall and attaching part of its door to it is not disbelief (kufr), because the building of the tomb itself—even though it is a reprehensible innovation (bid‘ah munkarah)—is not disbelief. The requirement is to explain the ruling on building tombs to people, spread awareness in this regard, and strive to level the tomb, making it like ordinary Muslim graves.