Improving Oversight of Women Veterans' Care Act of 2021 This bill requires the Department of Veterans Affairs (VA) to submit an annual report on women veterans' access to gender-specific services under arrangements entered into by the VA with non-VA medical providers for the provision of hospital care or medical services. The bill also requires the VA to establish a policy under which (1) the environment of care standards and inspections at VA medical centers include specified elements, and (2) no medical center is eligible for a five-star rating unless it meets the environment of care standards.