Gender bias in machine translation (MT) is recognized as an issue that can harm people and society. And yet, advancements in the field rarely involve people, the final MT users, or inform how they might be impacted by biased technologies. Current evaluations are often restricted to automatic methods, which offer an opaque estimate of what the downstream impact of gender disparities might be. We conduct an extensive human-centered study to examine if and to what extent bias in MT brings harms with tangible costs, such as quality of service gaps across women and men. To this aim, we collect behavioral data from 90 participants, who post-edited MT outputs to ensure correct gender translation. Across multiple datasets, languages, and types of users, our study shows that feminine post-editing demands significantly more technical and temporal effort, also corresponding to higher financial costs. Existing bias measurements, however, fail to reflect the found disparities. Our findings advocate for human-centered approaches that can inform the societal impact of bias.