TBH I thought she essentially telefragged the GI, by being transported to all the moments where it had just been transported to, and taking its place...
^ That is the best theory I've read on this and other sites about what happened. That Clara walking into the Doctor's timestream supplanted the GI and all the effects he brought on the universe. Clara being benevolent and harmless didn't interfere with the Doctor's on his adventures across the time and space. Clara is a vaccine to the GI's poison effects on the Doctor's life. I suppose you could infer that only one consciousness can exist simultaneously inside another person's timestream. I can buy that.