The paper is written on a further advancement of the operator partial conversion method for the problems of wave dissipation by plane ribbon shields. The regularization is made of paired integral equations of the sufficiently general kind, assigned in the material axis finite interval system. As a result, such Fredholm integral equations of the second kind are obtained on the entire axis that have the nuclei of simple enough structure. As an example, the problem is considered of the plane electromagnetic wave scattering by a limited ribbon grating, located on the vacuum-dielectric space interface. Studies are made on the H- and E-polarizations. The main terms of asymptotic expansions for the main dissipated field energy characteristics and surface current density on the grating ribbons are derived.