The dozens of middle-aged Iranians standing in six neat, gender-segregated rows stare straight ahead from behind the chain-link fence close to the entrance of Camp Ashraf, some 40 miles north of Baghdad in Diyala near the Iranian border. "Ashraf is our home, Ashraf is our home," they robotically chant in Iranian-accented Arabic, as they jab their right fists into the air in unison. Some of the women, who are all dressed in pantsuits with long jackets and colorful headscarves tied under the chin, carry placards in Persian. A bright yellow banner shimmers in the mid-morning sun. "Ashraf is the city of peace," it says in Arabic.

Most of the time there's nobody outside Camp Ashraf to hear the members of the Mujahedin-e Khalq (MEK), a fiercely anti-Tehran group who have been based...