Veterans Economic Recovery Act of 2020 This bill addresses the employment and retraining of veterans, specifically during the COVID-19 (i.e., coronavirus disease 2019) public health emergency. The bill requires the Department of Veterans Affairs (VA) to implement a program under which the VA must provide up to 12 months of nontransferable retraining assistance to up to 35,000 eligible veterans for the pursuit of a specified program of education. Under the bill, an eligible veteran is an individual who, among other requirements, is unemployed due to COVID-19. Veterans who receive retraining assistance may only use such assistance to pursue specified programs, including those designed to provide training for high-demand occupations. The Government Accountability Office must report on the outcomes and effectiveness of the retraining assistance program. The bill provides access to the National Directory of New Hires to the VA and the Department of Labor for the purpose of tracking the employment of veterans. The bill makes updates to the VA's High Technology Pilot Program, including by expanding the class of providers of high technology education programs. The bill reauthorizes and expands the program for the provision of off-base transition training for veterans and their spouses, including by requiring a preference for participation by states with economies significantly impacted by COVID-19. Finally, the bill implements a five-year grant program requiring the VA to make grants to organizations for the provision of transition assistance to members of the Armed Forces who are separated, retired, or discharged from the Armed Forces, and spouses of such members.