This is a very astute question because it identifies the massive differences in the way that Mama and Dee regard their past. In the story we are presented with a central matriarchal character who is intensely proud of the way that she and her immediate ancestors have made a life for themselves in the United States. She talks openly about her lack of education, partly because of the racism experienced as she was growing up. This is in complete contrast with Dee, who seized education as a way of leaving her humble roots, which it is obvious she is ashamed of, and tried to impose this education on Maggie and Mama:
She washed us in a river of make-believe, burned us with a lot of knowledge we didn't necessarily need to know. Pressed us to her with the serious ways she read, to shove us away at just the moment, like dimwits, we seemed about to understand.
Now, however, Dee has embraced her African roots, conveniently forgetting about the squalor and poverty of her life, changing her name. We most clearly see the differences in interpretation of the word "heritage" when we consider the conflict over the quilts. Note what Mama says about them:
They had been pieced by Grandma Dee, and then Big Dee and me had hung them on the quilt frames on the front porch and quilted them... In both of them were scraps of dresses Grandma Dee had worn fifty and more years ago. Bits and pieces of Grandpa Jarrell's paisley shirts. And one teeny faded blue piece, about the size of a penny matchbox, that was from Great Grandpa Ezra's uniform that he wore in the Civil War.
These are literally quilts formed of the history of Mama's family and predecessors, and yet to Dee they are just a novelty to be hung up and displayed as an object of beauty. To Mama's hard-working background, this is a betrayal of the spirit of her family and the daily grind that has featured their existence, which is why she rejects Dee's idea of her African heritage and rather gives them to Maggie, who understands her immediate family heritage.