We study and demonstrate the rephasing property of the echo response in a multilevel rotational system of iodomethane via long time-resolved optical birefringence measurements. The strong centrifugal distortion of iodomethane is utilized as a dephasing mechanism imprinted on the echo signal and is shown to rephase throughout its evolution. The dependence of the echo signal amplitude on the driving pulses' intensities is theoretically and experimentally explored. The analogy to Hahn's spin echoes is discussed, and a quantum-mechanical version of Hahn's track runners is provided for the case of multilevel rotational system.