We derive the leading backreaction of high-frequency gravitational waves on the Levi-Civita spacetime parametrized by the Komar mass density µ_K, using the Isaacson formalism with Brill–Hartle averaging. The high-frequency gravitational-wave amplitude decays radially independently of µ_K when expressed in terms of the cylindrical area radius, but acquires a mass dependence when expressed in proper radial distance. Both screen polarizations induce the same functional form of the quadratic wave terms entering the second-order Einstein equations. The polarization-summed Isaacson source obtained after Brill–Hartle averaging determines the evolution of the Rao metric function encoding the outgoing null radiation and the corresponding C-energy flux. Extending to general diagonal Einstein–Rosen backgrounds, we decompose the slowly varying potentials relative to the Levi-Civita seed and show how the Levi-Civita Komar charge is embedded in the Noether–Komar charge of the radiative spacetime, separating the static contribution from those of the Einstein–Rosen wave, its coupling to the background, and the high-frequency flux. At the Rindler endpoint, the limiting geometry depends on the asymptotic behavior of the high-frequency radiation: vanishing outgoing energy flux gives a locally flat limit, whereas a finite nonzero flux yields, for isotropic transverse geometry, a conformally flat pure-radiation pp-wave with nonexpanding, shear-free radiation rays.