Methods in the field of quickest change detection rapidly detect in real-time a change in the data-generating distribution of an online data stream. Existing methods have been able to detect this change point when the densities of the pre-and post-change distributions are known. Recent work has extended these results to the case where the pre-and post-change distributions are known only by their score functions. This work considers the case where the pre-and post-change score functions are known only to correspond to distributions in two disjoint sets. This work employs a pair of "least-favorable" distributions to robustify the existing score-based quickest change detection algorithm, the properties of which are studied. This paper calculates the leastfavorable distributions for specific model classes and provides methods of estimating the least-favorable distributions for common constructions. Simulation results are provided demonstrating the performance of our robust change detection algorithm. N the fields of sensor networks, cyber-physical systems, biology, and neuroscience, the statistical properties of online data streams can suddenly change in response to some application-specific event ([1]-[4]).