The template-fit approach is often used to separate Galactic dust emission from cosmic infrared background (CIB) anisotropies in low HI column density regions, under the assumption that gas and dust are tightly correlated. However, this method fails in regions where additional Galactic emission from molecular hydrogen, diffuse ionized gas, and dark gas is present. We develop and test a statistical component-separation method to extract the dust signal from contaminated textitPlanck 353 rm GHz observations using Scattering Covariance (SC) statistics. We first obtain a set of CIB maps over 25 square patches, each covering an area of 222 rm deg², using the linear correlation between dust and Galactic 21 rm cm HI emission, which is valid in low HI column density regions, through the template-fit approach. We then construct, from these 25 maps, a generative model of the CIB using SC statistics. Finally, we rely on this contamination model to perform component separation of dust and CIB in the textitPlanck data for different sky regions. Applying our algorithm to the textitPlanck 353 rm GHz observations, we recover a dust map for a test sky region that exhibits more structure than the corrected SFD map at 100 μ rm m. The differences observed at the map level can be explained by decomposing the recovered textitPlanck dust map into two gas phases: dust associated with N_HI and dust associated with N_(H₂). This work provides a clear pathway for mapping Galactic interstellar reddening over intermediate and high Galactic latitudes.