Marketing and Outreach Restoration to Empower Health Education Act of 2021 or the MORE Health Education Act This bill requires the Department of Health and Human Services (HHS) to conduct outreach and reporting related to federally facilitated exchanges (i.e., health insurance exchanges established and operated within states by HHS). The activities must inform potential enrollees of the availability of coverage and related financial assistance under the exchanges and must be provided in culturally and linguistically appropriate formats. The bill provides funding for the activities. Beginning for plan year 2022, HHS also must publish biweekly reports that include specified metrics about the performance of such exchanges during each annual open enrollment period. Further, after each open enrollment period, HHS must report on how many consumers enrolled in coverage with assistance from patient navigators, the advertising and outreach expenses related to raising awareness about open enrollment, and the amount of monthly user fees collected during the plan year.