One of the sneakiest real-world references found in "Avatar: The Last Airbender" is in Season 2, Episode 17, "Lake Laogai." The episode featured Team Avatar searching for the captured Appa. Thanks to the help of Longshot, Smellerbee, and a brainwashed Jet, the team found and entered a secret base under Lake Laogai, run by the Dai Li – a faction within Ba Sing Se. There they stumble upon a group of brainwashed women acting as clones of Joo Dee, a Ba Sing Se official who the Dai Li brainwashed to neutralize unwanted guests (via IMDb).
The real-world connection found in this episode is the name of Lake Laogai. Laogai is short for Laodonggaizao, which means "reform through labor." Laogai was a criminal justice system that established penal labor camps and prison farms known as laogai camps throughout the People's Republic of China in the 1950s. The goal of the laogai camps was to reform criminals into law-abiding citizens through forced labor (via Laogai Research Foundation).
The camps were renamed prisons in 1994, and the Chinese government had an extensive network of labor prisons that produced commercial goods to export to the United States and Europe. Former Chinese political prisoners established the Laogai Research Foundation (LRF) to combat the forced labor system. One report that they released estimated the country had over 1,000 working laogai facilities. The Chinese government abolished the system in 2012 after an Al Jazeera documentary exposed the country's inhumane treatment of prisoners (via LRF).