Does Grete Change in the course of The Metamorphosis? If so how does she change?
Yes, Grete changes quite a bit. Initially, she is the person who takes care of Gregor, and she seems to really care for him too. When she notices that he has not eaten the milk and bread she left him, she responds in a really thoughtful way:
To find out his likes and dislikes, she brought him a wide assortment of things, all spread out on an old newspaper: old, half-rotten vegetables; bones left over from the evening meal, caked with congealed white sauce; some raisins and almonds; a piece of cheese, which two days before Gregor had declared inedible; a plain slice of bread, a slice of bread and butter, and one with butter and salt.
Grete treats Gregor kindly, taking the time to offer him a veritable smorgasbord of food and food-type items in order to figure out what will satisfy him in his new form. He is so grateful to her that his eyes are actually "streaming with tears of contentment." Gregor isn't used to being treated so nicely, even prior to his metamorphosis, and Grete is going out of her way to try.
Later on, Grete gets a job at a store in order to help the family financially, and this often leaves her exhausted, with less and less time for Gregor. The family began using his room for storage when they had to take in boarders to help cover their costs. "Whatever was not being used at the moment was just flung into Gregor's room [...]." Finally, as more time goes by, Grete comes to view Gregor as too much of a burden on the family. She says,
"My dear parents [...], things can't go on like this. Maybe you don't realize it, but I do. I won't pronounce the name of my brother in front of this monster, and so all I saw is: we have to try to get rid of it."
She has come to believe that the animal she sees is not Gregor. She reasons, "'If it were Gregor, he would have realized long ago that it isn't possible for human beings to live with such a creature, and he would have gone away of his own free will." In the end, Grete seems much more capable and self-sufficient than she did in the beginning, but she is not as kind, and -- with a job of her own now -- she is much less willing to spend any time catering to the whims of an animal who may or may not be her brother.
Grete Samsa, Gregor's sister, most definitely goes through a "metamorphosis" as does every member of the family. Before Gregor's change, Grete is described as a "useless" daughter. She has taken violin lessons, but she isn't very good. She doesn't leave the house often. She is timid and seemingly afraid of the world. She "whispers" and "wimpers" at Gregor's door to get him to get up and come out to breakfast. The entire family depends on Gregor for their well-being and existence.
She is a good soul, however, as she is the one who takes care of Gregor when his secret is discovered. She is afraid of him in his new state, but she attempts to be caring and kind.
After Gregor's change, Grete also gets a job outside of the house. She is stepping into Gregor's role of caretaker of the family. However, because of her new duties, she also begins to neglect Gregor and her caretaking duties of him. Even so, she displays an uncharacteristic anger when their mother cleans Gregor's room while Grete is away from the house.
Although at the beginning of the story Grete seems to have the closest and most loving relationship with Gregor, she is the one who argues most vigorously for getting rid of him.
So, change is not always a good thing. In Grete, she has discovered independence, but she has become colder and less loving as a result. Oddly enough, her parents see her as growing into her womanhood and declare she is ready for a husband.