I think the thing people are most scared of is how the Republicans will use it against her, since they won't really be looking at the nuance of the situation.
What I know is that while claiming that heritage one of the controversial issues was that Harvard promoted her as a historic woman of color professor and there are questions about whether she used that heritage claim to her personal benefit.
She has since apologized for it and insisted she did not use it for personal gain. I don't think it's a good thing to use against her but again, the worry is how Republicans and especially Trump will use it vs her especially with the nickname he's given her "Pocahontas."
I wasn't aware of the issue with Harvard (and if that's the case that's definitely a pretty scummy thing to do, but everyone has skeletons in their closet, and it seems like a minor issue next to the fact that the standing president openly brags about, if presented in the most favorable possible light, using his fame and influence to coerce women into sexual encounters that they otherwise wouldn't consent to). As for Trump and co. holding that against her, I really don't think it's an issue that's going to sway many voters. Most of the people calling her Pocahontas and the like weren't voting for her to begin with.