She didn't to let her maternal family know. Yet...plus her grandmother was hoping her mother had a happy life, so she lied about her status. telling them she was the princess of the overthrown royalty would have complicated a lot of things. This is what i think
She lied to them. I'm guessing there were two reasons for this. One, because it would complicate things if they knew she was/is a princess of Tang. And two, her uncle and grandmother are already grieving. If she told them that her mother suffered during the time she was alive, they would feel even worse.
Wait isnt she a junzhu(princess) then why would she said that she's the daughter of a sui general/captain?