I have same problem. I was able to remove the chapter labels by going into the ATV settings and turning subtitles on, then back off. Did the same for closed captioning... not sure which one fixed it, but labels are gone when you resume the movie. Good Luck.
-Does anyone have a problem with the chapter titles popping up while the movie is playing and staying on the screen? Happens with each chapter. Subtitles are checked off, but they are not subtitles. Never in the 4 years has happened before and this was with the movie rental Argo. Afraid to rent another movie with the same thing happening. Ps, the title does disappear when you rewind, but as soon as the next chapter starts, that title pops up and stays up. Any help would be great!