Pupillometry, increasingly popular in cognitive and neural science due to its strong ties to cognitive factors and advancements in measurement techniques, faces challenges in methodological understanding, particularly regarding factors that could threaten measurement validity. One such factor is eye blinking, which occurs frequently and is influenced by various cognitive components. Blinking induces a pulse-like pupillary change, known as the "blink-locked pupillary response (BPR)," which includes constriction and dilation phases with significant magnitude and duration. Our study aimed to characterize the basic properties of BPR, including its shape, magnitude, and variability across subjects and blinks, to understand its potential confounding effects on pupillometry. We demonstrated how cognitive dependency of eye blinking can confound pupillary responses through BPR, potentially misrepresenting the cognitive states intended to be measured. By constructing a statistical model of these confounding effects, we developed a probabilistic-inference algorithm to de-confound raw pupillary measurements. This algorithm effectively removed BPR and enhanced the statistical power of pupillometry experiments. Our findings highlight the need to consider and address BPR in pupillometry studies, and our proposed algorithm offers a robust solution for mitigating the confounding effects of BPR, ensuring more accurate and reliable measurements.