Plasmons in two-dimensional semiconductor devices will be reflected by discontinuities, notably, junctions between gated and non-gated electron channels. The transmitted and reflected plasmons can form spatially- and frequency-varying signals, and their understanding is important for the design of terahertz detectors, oscillators, and plasmonic crystals. Using mode decomposition, we studied terahertz plasmons incident on a junction between a gated and a nongated channel. The plasmon reflection and transmission coefficients were found numerically and analytically and studied between 0.3 and 1 THz for a range of electron densities. At higher frequencies, we could describe the plasmons by a simplified model of channels in homogeneous dielectrics, for which the analytical approximations were accurate. At low frequencies, however, the full geometry and mode spectrum had to be taken into account. The results agreed with simulations by the finite-element method. Mode decomposition thus proved to be a powerful method for plasmonic devices, combining the rigor of complete solutions of Maxwell's equations with the convenience of analytical expressions.