The drive comes under a state law that allows a majority of parents at a failing school to force it to make major changes.
Romero and Hidalgo claim their children's' teachers harassed the youngsters about their parents' activities.
Compton Unified School District said it hasn't been contacted by any agency investigating the complaint.
However, the district issued a statement, saying "We have zero tolerance for harassment. We take all allegations of harassment seriously, particularly if those allegations involve a staff person or teacher employed by our district."