We introduce the Differential Matched Filter (DiffMF), a computationally efficient extension to the Matched Filter (MF) designed to distinguish genuine Greenhouse Gas (GHG) enhancements from false enhancements. Conventional MF retrievals are often plagued by high-magnitude false concentrations driven by surface or atmospheric features that mimic the target absorption. DiffMF exploits the inherent functional characteristics of wavelength-varying spectroscopic observations—specifically, the derivatives of the whitened target and observed spectrum with respect to wavelength—to address the numerical ambiguities at the source of these artifacts. We validate this approach on a dataset consisting of 900 EMIT scenes containing 389 expert labeled CH₄ plumes and 5,763 "plume-like" false plume detections, and demonstrate that simple metrics derived from our DiffMF retrievals provide an effective means to discriminate real GHG-enhanced pixels from false enhancements, to reject of false positive plume detections, and to guide iterative refinement of background covariance estimates without compromising the broadly effective filtering capabilities provided by the conventional MF. We further present preliminary results extending DiffMF to the retrieval of other GHG species including CO₂, NO₂, and NH₃. To facilitate adoption across imaging spectroscopy instruments, platforms, and applications, we provide a complete Python implementation for reproducibility.