There is often a lack of consistency in the footprints between satellite observation data, as well as between satellite observations and numerical models. This mismatch is typically caused by the different spatial resolutions of observed data in multiple frequency channels. The Backus–Gilbert inversion (BGI) algorithm is widely used for brightness temperature remapping in various microwave payloads to make the observation footprints more consistent. The microwave radiation imager for the rainfall mission onboard FengYun-3G introduces a novel integration of imaging and sounding channels for precipitation monitoring. However, this integration presents challenges in the matching of observation footprints, as they exhibit not only the conventional discrepancy in footprint sizes but also a misalignment between the center locations of the footprints of the sounding and imaging channels. This article proposes an improved BGI algorithm to match the observation footprints from sounding channels with those from imaging channels in terms of both spatial resolution and location. This study uses a distance-based fixed window for the filtering of source observations and employs an automatic noise parameter selection scheme to strike a balance between the fit error of footprints and noise. A coefficient reuse method is applied to improve computational efficiency. The experimental results using simulated data demonstrate that our improved BGI algorithm leads to a significant decrease in the overall root mean square error by 80% and 50% in the clear-sky and typhoon cases, respectively, compared to the raw ${{T}_A}$. The remapping results of real observations demonstrate that our algorithm effectively suppresses noise in each channel.