We show exemplary initial metrics for gravitational axial waves, that are twice differentiable but which are not $C^2$. They generate wave pulses that interact with matter in the radiation cosmological era. This forces the radiation matter to rotate. This rotation is permanent - it persists after the passage of the gravitational pulse. In contrast to that, we explicitly show that a class of smooth initial metrics that are at least $C^2$ gives rise to gravitational wave pulses that do not interact with the background during the radiation epoch.