Optical injection locking of a metasurface quantum-cascade (QC) vertical-external-cavity surface-emitting laser (VECSEL) is demonstrated at 2.5 THz using a Schottky diode frequency multiplier chain as the injection source. The spectral properties of the source are transferred to the laser output with a locked linewidth of ∼1 Hz, as measured by a separate subharmonic diode mixer, and a locking bandwidth of ∼300 MHz is achieved. The large locking range is enabled by the microwatt power levels available from modern diode multipliers. The interplay between the injected signal and feedback from external reflections is studied and demonstrated to increase or decrease the locking bandwidth relative to the classic locking range depending on the phase of the feedback.