It's been a little while, but I found I had that problem if I was watching any achievements. Whenever I would log into a character, /reload, or switch zones the Blizzard quest watch would show up. Now, I keep my Carbonite Quest Watch window fixed size and minimized, so all I had to do was maximize, then minimize, it and Blizzards quest watch went away. Until I would change zones or did something and I had to /reload my UI, or switched toons. Then it came back. I finally installed
WatchFrameRemover to solve the problem with my set up.