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It is difficult to say with any sort of certainty, but it is definitely clear that Grete represents a sympathetic attachment with Gregor--even if that does change at the end of the story. I'd say that Grete refrains from speaking to him in order to avoid encouraging the despair that he would no doubt feel as a result of not being able to respond.
Grete attempts to care for Gregor in the same way he used to care for her, but she seems driven by family duty rather than a true human bond, as we see from the fact that she never addresses Gregor directly except on one occasion when she turns to threaten him. Grete seems to think that Gregor cannot understand her, though he gives clear signals (somehow invisible to her) of his intelligence and concern for her.
She feels very awkward about the situation of Gregor turning into a vermin. She feels that his appearance is now grotesque and he seems pretty useless. She thinks Gregor causes trouble to the family such as to her mom and dad. She doesn't treat him as if he was truly in the family.