Several studies suggest that during the early pandemic, amidst socioeconomic instability, children from underserved families were more likely to resort to consuming cheaper, lower-quality foods with longer shelf lives. This study investigated the change in unhealthy food consumption across different phases (pre, early, mid) of the COVID-19 pandemic, and whether the strength of association between unhealthy food consumption and household socioeconomic disadvantage (HSED) varied across phases of the pandemic. This study utilized serial cross-sectional data collected from low-income families enrolled in a school-based food co-op, Brighter Bites. Secondary data analysis included 5,384 surveys from families who had complete data: 3422 pre-pandemic, 944 from the early pandemic, and 1,018 mid-pandemic. Outcome measures included sugary food intake and convenience/fast food intake, each of which was operationalized as a scale using pre-validated items from the surveys. HSED was operationalized as a composite of parent employment, parent education, food insecurity, and participation in government programs; responses were categorized into low, medium, and high HSED groups for analysis. We examined the interaction between HSED and time period to explore how HSED and its association with dietary measures changed over the course of the pandemic. A significant linear negative trend, i.e., a decrease in consumption from pre-to-mid-pandemic period was seen in sugary food intake (p < 0.001), but not in convenience food intake. In data pooled across time-periods, both sugary food and convenience/fast food consumption were inversely associated with HSED, and low unhealthy food consumption was observed among high-disadvantage groups. No significant interaction between time period and HSED was observed on either scale. However, the post-regression estimates from the adjusted interaction model showed a significant association between convenience/fast food consumption and HSED in pre- and mid-pandemic periods. The study highlights the nuances of socioeconomic dynamics on the diet behaviors of children from low-income families during a natural disaster.