Coronavirus Oversight and Recovery Ethics Act of 2020 or the CORE Act This bill establishes requirements for oversight, accountability, and transparency in the disbursement and supervision of COVID-19 (i.e., coronavirus disease 2019) relief funds. Among other things, the bill prohibits conflicts of interest in the selection or hiring of contractors or advisors and in the distribution of relief grants and loans; allows inspectors general to be fired only for specified reasons; grants the Congressional Oversight Commission, established in the Coronavirus Aid, Relief, and Economic Security Act (CARES Act), subpoena authority for testimony and documents and expands its jurisdiction to include all COVID-19 relief funding, including the Paycheck Protection Program (PPP) of the Small Business Administration (SBA); requires the Department of the Treasury to submit a weekly list of any instances in which the Special Inspector General for Pandemic Relief or the Pandemic Relief Accountability Committee believe the executive branch has unreasonably denied them information; requires lobbyists to make monthly disclosures regarding all lobbying related to COVID-19 relief spending or lending; establishes whistle-blower protections for government contractors and private sector workers who may witness waste, fraud, or abuse or be victims of misconduct; requires the SBA to publicly disclose information about PPP lenders and recipients, including loan amounts; and allows any individual harmed by a company's misuse of industry stabilization funds to seek recourse through the courts.