The Atlantic has a nice set of pictures of the Great Wall up, for your teaching pleasure. The one I found most interesting is this.
Is the Great Wall on fire? Well, the caption says “Smoke rises from a watchtower of the Great Wall during an activity to mark the International Anti-Drug Day in Beijing, on June 26, 2006” There is an old tradition of burning stuff in China, but mostly as a form of worship. In the late Qing, however, missionaries and Chinese reformers began to make burning opium and opium paraphernalia a regular part of their rituals. Here is one from Fujian1
Opium and drug burnings became a regular part of Chinese anti-opium events, but as far as I know the whole burning things in protest meme never caught on as a general method of protest in China. Eventually this form of anti-opium protest became engrained enough in Chinese political culture that it traveled back in time. Lin Zexu had -destroyed- opium in 1839, and by 1909 he was credited with burning it, as in this image2 This mistake is now pretty common. 
I’m not really a 19th century person, so I never put much effort in to figuring out when this form of protest emerged. It does not seem to link up well with the Chinese tradition of burning things as an offering, since you burned things you thought the ancestors would want. Admittedly, by 1909 some of your ancestors probably would have liked some opium, but that does not fit in with the protest aspect of things. Maybe a legacy of Guy Fawkes day in England? In any case, if you want to burn something in the name of China, the Great Wall would seem a great place for it.
Seems more like a Temperance Union thing — they liked to smash barrels and break up saloons — than a Chinese thing. Connection to missionary reformers?
Yeah, I assume it came from the missionaries as they were all over in the early anti-opium movement. I’ve never found anything on who first came up with the idea or why they thought it was good, but it sure spread in a hurry.