What it shows is that their relationship is not at all tight nor deep deep, and, how could it be? Poor Gregor's life is so focused on work and on his consistent routine that it renders him unable to establish any true and meaningful human connections. This shows how Kafka intends to present the superficiality of society: By giving us a very complex, fantastic, and nonsensical situation spoken under the perspective of characters who are unable to think something other than life as he knows it. In addition to the shallow ties of the family, we also learn about the obliviousness with which the family takes Gregor's changes.
They basically focus on the tediousness of the situation rather than on Gregor's well-being. Like the previous post noted, they literally shut the door on Gregor. They established a clear difference between them and Gregor. The family made sure that they were in no way connected to him emotionally, psychologically, or even as a family. Even Gregor, himself, had a massive disconnect between himself and his situation. The door is the symbol of that family divide. Gregor will exist and cease to exist in his own little world in the bedroom. Meanwhile, life goes on as usual for the family, separated from Gregor.