Parental involvement in traditional autism therapy is key to the effective treatment of children with ASD. Little is known about parental involvement in robot-assisted autism therapy (RAAT)--novel therapeutic support for children with ASD. Our study investigates the effect of parental presence on multiple-session RAAT conducted with 16 children with ASD. They interacted with the social robot in the presence or absence of their parents. We measured children's socio-behavioral outcomes and conducted semi-structured interviews with parents. Parents did not necessarily affect the children's outcomes during the interventions. However, children's autism-related symptoms resulted in different socio-behavioral outcomes between sessions with and without parents. Most parents have reported positive changes in their children's behaviors when interacting with the robot.