The full question is "What do you think, considering the newer evidence found this year, regarding Mary Carey's children and the possibility of the two children actually being Henry VIII's? What do you think Anne felt about this?" - Ooooh tough one! It's always been debated whether Henry was father to both of Mary Boleyn's (Carey's) children, so I don't think that this is a surprise, although people are still arguing about this! I think Anne would have accepted that Henry had had previous relationships and she would have known about Bessie Blount's son too. The Boleyn family were a close family so she would have known the truth about Mary and her children from the beginning, but it must have been weird for her forming a relatonship with a man who had been so intimate with her sister. Anne wouldn't have been human if she had not been jealous of how easy her sister had had children, when she herself was having miscarriages and couldn't give Henry his longed for son.
There's an interesting article on whether Henry VIII was the father of Mary Carey's children see http://newsgroups.derkeiler.com/pdf/Archive/Soc/soc.genealogy.medieval/2008-10/msg00618.pdf. I've also just written https://www.theanneboleynfiles.com/did-henry-viii-father-mary-careys-children/965/