Previous research has shown mixed evidence on the associations between mobility data and COVID-19 case rates, analysis of which is complicated by differences between places on factors influencing both behavior and health outcomes. We aimed to evaluate the county-level impact of shifting the distribution of mobility on the growth in COVID-19 case rates from June 1 - November 14, 2020. We utilized a modified treatment policy (MTP) approach, which considers the impact of shifting an exposure away from its observed value. The MTP approach facilitates studying the effects of continuous exposures while minimizing parametric modeling assumptions. Ten mobility indices were selected to capture several aspects of behavior expected to influence and be influenced by COVID-19 case rates. The outcome was defined as the number of new cases per 100,000 residents two weeks ahead of each mobility measure. Primary analyses used targeted minimum loss-based estimation (TMLE) with a Super Learner ensemble of machine learning algorithms, considering over 20 potential confounders capturing counties' recent case rates as well as social, economic, health, and demographic variables. For comparison, we also implemented unadjusted analyses. For most weeks considered, unadjusted analyses suggested strong associations between mobility indices and subsequent growth in case rates. However, after confounder adjustment, none of the indices showed consistent associations after hypothetical shifts to reduce mobility. While identifiability concerns limit our ability to make causal claims in this analysis, MTPs are a powerful and underutilized tool for studying the effects of continuous exposures.