This study addresses the detection of gunshot residue (GSR) around a bullet hole, which is one of the key forensic procedures for estimating firing distance. GSR was inspected using Flash-Pulse Thermography (FPT) with kurtosis statistical processing. The result of such an inspection is a pattern composed of numerous small indications distributed around the hole, attributed to gunshot residue particles. The number and spatial distribution of these indications depend on the firing distance. Analyzing such results based on individual indications is impractical, as the pattern must be evaluated as a whole. Therefore, quantifying the overall result can significantly improve the analysis of the firing distance estimation. This study presents a quantification procedure based on threshold-based mass-marking of indications and evaluation of several statistical characteristics. The correlation between these characteristics and firing distance is then analyzed. A strong but distinctly nonlinear correlation was found between the firing distance and some simple quantitative characteristics, such as the total number of indications. However, the study shows that some derived characteristics, such as the contrast between marked areas and background, exhibit a near-linear correlation. These parameters are, therefore, promising for firing distance analysis based on FPT inspection of GSR on through-shot targets.