In one aspect, a system for controlling an operation of an actuator mounted on a seed planting implement may include an actuator configured to adjust a position of a row unit of the seed planting implement relative to a toolbar of the seed planting implement. The system may also include a flow restrictor fluidly coupled to a fluid chamber of the actuator, with the flow restrictor being configured to reduce a rate at which fluid is permitted to exit the fluid chamber in a manner that provides damping to the row unit. Furthermore, the system may include a valve fluidly coupled to the flow restrictor in a parallel relationship such that the valve is configured to permit the fluid exiting the fluid chamber to flow through the flow restrictor and the fluid entering the fluid chamber to bypass the flow restrictor.