Responsible Education Mitigating Options and Technical Extensions Act or the REMOTE Act This act addresses the administration of certain Department of Veterans Affairs (VA) educational assistance benefits. First, the act extends through June 1, 2022, certain adjustments for veterans' education benefits that were put in place due to COVID-19. The act allows the VA to waive the requirement that an educational institution verify the enrollment of a student utilizing VA educational assistance if the VA determines the institution uses a flat rate tuition and fee structure that would make the use of a second verification unnecessary. The act provides an exception from the imposition of specified disciplinary actions (e.g., suspending course and program approval) in situations where an educational institution provides a commission, bonus, or other incentive payment to entities engaged in student recruiting or admission activities related to recruiting foreign students who reside in foreign countries and are ineligible for federal student assistance. Additionally, the act generally exempts from certain requirements and restrictions imposed by the VA or a state approving agency educational institutions (1) located in foreign countries, or (2) that provide information regarding the costs of a program of education using a form or template developed by the Department of Education. The act also exempts educational institutions located in foreign countries from (1) having records and accounts that pertain to an individual who is not receiving VA educational assistance examined by government representatives, and (2) furnishing certain information related to tests that require payment. The act authorizes the VA, in certain circumstances, to provide educational assistance (including a housing stipend) to veterans or eligible persons who are in their last academic period (e.g., semester) of a program of education and are pursuing the program on less than a half-time basis. Specifically, such assistance may be provided if the number of credits the person needs to complete the program of education is less than the number of credits that would constitute enrollment on more than a half-time basis for that last academic period and the person (1) is enrolled in or has completed every course offered by the program of education during that academic period, and (2) enrolls in an additional course that is not required for the program of education to reach enrollment on a more than a half-time basis. The act extends certain loan fee rates through January 14, 2031, under the VA's home loan program. Finally, the act removes the cap on the number of full-time VA employees who provide equal employment opportunity counseling.