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We have solved the problem of diffraction of terahertz (THz) radiation on perfectly conductive gate strip that partially screens a two-dimensional (2D) electron layer located at some distance from the gate. Scattering and absorption spectra of such a structure reveal the fundamental plasma resonance excited under the gate. We have shown that the absorption enhancement factor at plasma resonance may reach very high values (up to 60). However, for narrow gate strips (with the width less than 100 nm) the resonant scattering length of such a scatterer is shorter than its resonant absorption length by 4 orders of magnitude, which means that the gated plasmons in this case weakly couple to the THz radiation. We discuss the effects of interaction between plasma oscillations in gated and ungated regions of 2D electron layer and provide a qualitative explanation of rather intensive THz emission from unstable gated plasmons in a 60-nm gate field-effect transistor observed recently.