In terahertz (THz) detectors, based on the excitation of electron plasma oscillations in the two-dimensional electron gas (2DEG) channel, the incident electromagnetic wave is repeatedly reflected between the metal-coated back surface of the GaAs substrate and top surface of the detector. Under certain conditions, a standing terahertz (THz) wave can be established. Placement of the 2DEG in the antinode of the standing wave can result in strong absorption of the detecting THz radiation as we confirmed by analytical calculations and experimental measurements of frequency dependences of THz reflection and absorption coefficients. Effects of the metal bus connecting the fingers of the grating-gate and thickness of the GaAs substrate on the performance of the THz detector were studied as well. It was demonstrated that the spatial separation of the gate fingers from bus metallization by the mesa resistor resulted in the enhanced photoresponse of the detector.