The Regulators are the well-armed militia of Lena's world. They have the power to violate everyone's privacy—they can go onto their property, search them, run ID checks—and they abuse it every chance they get.
The men Lena briefly meets during her encounters with the Regulators look like they enjoy it, too. Not that we want to make this dystopian system work, but giving a bunch of average men weapons, and the go-ahead to abuse them, totally breaks the system.
Lena doesn't realize this, though. She parrots, "They exist for our protection, for our own good" (6.75). And even during the ID checks and the raids, she has no problem giving away her liberties in exchange for safety. Only when they impede Lena's pursuit of love—by trying to keep her away from Alex—does she realize that her safety isn't exactly their highest priority.