Non-covariance of "covariant polymerization" in models of loop quantum gravity

A new modification of spherically symmetric models inspired by loop quantum gravity has recently been introduced by Benitez, Gambini and Pullin, who claimed that it preserves general covariance. This claim is shown here to be incorrect, based on methods of effective line elements. The same methods imply that the only novel physical effect introduced by the modification is the presence of time-reversal hypersurfaces between classical space-time regions.