Gregor has a complex set of emotions towards his family. His feelings towards them, however, change far less than their feelings toward him.

Throughout the story, Gregor has a great sense of duty and concern for his family. He is willing to sacrifice his needs for their benefit. He also feels love towards them, mingled with resentment that he has to work in a dehumanizing job that he loathes as a traveling salesman to help pay their debts.

This sense of mingled duty, love, and resentment does not change much during the course of the novella. However, his family does change toward him, including his beloved sister Grete. They all grow increasingly to fear and resent him as a drag on their lives once he takes on an insect form and no longer can either work or speak to them. Grete expresses the family's feelings near the end, when she says he is no longer their Gregor. If he was, she says, he would have realized how hard the situation was and left them already. Instead, she says, they have to face that they have to get "rid" of the insect that used to be her brother.

Gregor, however, is still himself inside. If anything, released from his exhausting job and the resentment that it caused him, he feels more love than ever for his family. Injured and in pain from the apple lodged in his back and weakened because of not eating, he willingly and easily lets himself die for his family and is found not by his family members, but by the cleaning lady.

Early on, Gregor feels that his sister, Grete, is worrying unnecessarily.  He thinks that "[he] was still here and hadn't the slightest intention of letting the family down."  Gregor sees himself as the thing that has kept the family afloat all this time, and he feels an obligation to get everything back on track with his job.  He only begins to learn after his metamorphosis that the family's situation was not as dire as he believed it to be.  He sees, on the first day of his changed self, that "the breakfast dishes were laid out lavishly on the table" and that several newspapers were laid out for his father to read.  Also, he sees how late his family gets to sleep and becomes newly aware that neither his parents nor his sister have to work.

Later on, Gregor learns that his father has actually been saving some of the money that he has brought home.  "Of course he actually could have paid off more of his father's debt to the boss with this extra money, and the day on which he could have gotten rid of his job would have been much closer, but now things were undoubtedly better the way his father had arranged them."  Despite the fact that Gregor's father has, essentially, cheated him out of time, Gregor is not angry.  If anything, he now admires his father more as a result of his father's foresight.  Now, though, instead of feeling vital to his family's success, he begins to feel "hot with shame and grief" whenever they begin to talk about the need to earn money.

Soon after, Gregor's family begins to view him as more and more of a burden, and this affects the way Gregor views himself.  "Who in this overworked and exhausted family had time to worry about Gregor any more than was absolutely necessary?"  Gregor feels conflicted in regard to their treatment and irritability.  At times Gregor feels badly, and "at other times he was in no mood to worry about his family, he was completely filled with rage at his miserable treatment."  Gregor feels himself changing as a result of his family's treatment, though "it hardly surprised him that lately he was showing so little consideration for the others; once such consideration had been his greatest pride."  There are lots of ways in which Gregor's feelings toward his family have changed.

Gregor has a complex and conflicted relationship with his family. When the story opens, we see that his family are dependent on his salary, and therefore he feels very anxious to live up to his responsibilities and not do anything to jeopardise his job. However, when he turns so inexplicably into a giant insect, he can no longer do this and feels shame and guilt that he can't help his family any longer.

Along with this, though, he also feels gratitude when his sister helps him out in his new, strange condition. She does her best to look after him, and his mother, too, still seems emotionally attached to him. It is a different matter with his father, however; evidently the relationship between the two has always been difficult. (This reflects Kafka's strained relationship with his own father.)

As time goes on, however, and Gregor becomes weaker and more immobile, the situation with his family also deteriorates, and he starts to feel neglected by them. As he remains trapped in his room, even his sister ends up wholly resenting him, seeing him no longer as her brother, but as a monstrous burden on all the family. Gregor, too, comes to accept this opinion, and eventually wills himself to die, feeling that it will be a relief both to himself and his family. He still feels enough affection for them that he wants to perform this last self-sacrifice for them:

 He remembered his family with deep feelings of love. In this business, his own thought that he had to disappear, was, if anything, even more decisive than his sister's.

Certainly the family seem to experience a feeling of deep release after his death. This is the most troubling aspect of the story: the implication that the family are ultimately better off without Gregor. 

Interesting question! In the story “The Metamorphosis” by Franz Kafka, Gregor’s transformation greatly impacts his feelings about his family.

Initially in the story, Gregor demonstrates the profound responsibility that he feels toward his family. His feelings seem to be largely based on his belief that his family is incapable of taking care of themselves. For example, he believes that they cannot work because his father is too old, his mother is too frail, and his sister is too young. Thus, he works arduously at a job that he hates. As Gregor’s thoughts reveal:

“If I didn’t hold back for my parents’ sake, I would’ve quit ages ago. I would’ve gone to the boss and told him just what I think from the bottom of my heart. He would’ve fallen right off his desk!”

“...what a demanding job I’ve chosen! Day in, day out on the road. The stresses of trade are much greater than the work going on at head office, and, in addition to that, I have to deal with the problems of traveling, the worries about train connections, irregular bad food, temporary and constantly changing human relationships which never come from the heart. To hell with it all!”

As the story progresses, Gregor realizes that he can no longer provide for his family and now feels as though he is a burden to them. He relies on his family to clean his room, move furniture, and even to bring him food for each meal. Not only this, but he realizes that his new form scares his family and he feels responsible for protecting them from himself.

Finally, the story draws to a conclusion when Gregor realizes how much of a burden he has become to his family.

“But Gregor did not have any notion of wishing to create problems for anyone and certainly not for his sister.”

Thus, Gregor goes to his room and quietly passes away. After this event, his family grieves their loss; however, they also experience more freedom and become more self-sufficient.

In conclusion, Gregor’s transformation caused his feelings to change about his family. Although he first feels responsible for their well-being, he soon sees himself as a burden to his family. As a result, their roles have changed and he perceives that transition.

It is clear that as the story develops and Gregor becomes more and more used to his condition as a bug, his feelings of love and compassion towards his family fade and he becomes more and more selfish and focused on his own concerns and his internal world. Note for example what Gregor does when he sees his sister arguing with their parents about the deep cleansing that their mother has just carried out of Gregor's room:

...Gregor hissed loudly in his fury because no one thought of closing his door to shield him from this spectacle and commotion.

Gregor then appears to become more and more selfish as the story progresses. At the beginning of the story, it is clear he cares very deeply for his sister and his parents, and indeed lives his whole life trying to provide for them. At this point in the novel, it is clear that this selflessness has been replaced by a certain amount of selfishness that dominates his character.