Mental illness screening instruments are increasingly being administered through online patient portals, making it vital to understand how the design of digital screening technologies could alter screening scores. Given the strong cross-cultural belief in the gender depression disparity, digital screening technologies are at particular risk of triggering stereotype threat, the phenomenon where a reminder of a stereotype impacts task performance. To assess this risk, we investigate if a reminder about the gender depression disparity influences the scores of digitally administered mental screening instruments. In a comprehensive study, we collect data from 440 participants with a mobile application that reminds half of the participants of the gender depression disparity prior to administering depression and anxiety screening instruments. Our statistical analysis evaluates differences in screening scores with t-tests, and determines credible values for difference of means, of standard deviations, and effect size using Bayesian estimation. While the gender depression disparity reminder had no statistically significant impact on men, it did alter the depression screening scores of women and nonbinary participants. Further, prior depression treatment increased the impact of stereotype threat on women. Our research demonstrates that digital screening technologies are subject to stereotype threat and should thus be designed to avoid biasing mental illness screening scores.