I don't recall the Secret History of the Mongols even mentioning the Great Wall. It's been a while since I read it though.
Based on my understanding of the Wall and the Mongols, the Great Wall actually played a pretty minor roll in stopping them. They either some how managed to get around it or even bribed the guards to let their armies pass. Or they climbed it and took over. They pretty much probably Mulan'd the wall.
Or they smashed it and passed through because at the time China was fighting itself again with the Northern Song fighting the Southern Song so it's not like anyone noticed Genghis Khan's pyramid of skulls being built up just on the other side.
