I thought that she screamed the name of the sword "Ice". If anything, Ned's sword is the only thing that could convince Cat-zombie, because she is definitely not herself. Brienne's sword has a meaning only because it was made of a piece of Stark's Ice (f*ck Tywin for that...twice...) and it was given to her to protect Ned Stark's daughter (I was so touched when Jaime did this).