Polycrystalline PbSe for mid-wave infrared (IR) photodetectors is an attractive material option due to its high operating/ambient temperature operation and relatively easy and cheap fabrication process, making it a candidate for low-power, small footprint, uncooled/passively cooled photodetectors. However, there are many material challenges that reduce the specific detectivity (D*) of these detectors. In this work, we demonstrate that it is possible to improve upon this metric by externally modulating the effective lifetime of conducting carriers by application of a back-gate voltage that can control the recombination rate of carriers in the detector by increasing the passivation of PbSe. We build a back-gated PbSe detector, in which we experimentally observe unambiguous signature of effective carrier modulation with a back-gate voltage for different temperatures. We develop a quantitative model for the detector that captures and closely benchmarks this modulation, which is then used to project the increase in D* in better optimized detector designs. This approach when combined with other techniques, such as plasmonic enhancement of light absorption, can lead to substantive enhancement of performance in PbSe mid-wave IR detectors widening their application space.