We theoretically investigate the homogenization of the dielectric response to transverse electric waves of a transverse grating characterized by the Kapitza condition; i.e., the permittivity is rapidly modulated with a modulation depth scaling as the large wavelength-to-modulation-period ratio. We show that the resulting effective dielectric permittivity, in addition to the standard average of the underlying dielectric profile, has a further contribution arising from the fast and deep dielectric modulation. Such a contribution turns out to be comparable with the other one and hence can provide an additional method for designing dielectric metamaterials. As an example, we discuss an effective metal-to-dielectric transition produced by the Kapitza contribution obtained by changing the grating depth, a remarkable result for applications involving epsilon-near-zero metamaterial design.