Trademark Modernization Act of 2020 or the TM Act of 2020 This bill makes several changes to trademark law, such as by providing new mechanisms for opposing and canceling trademark registrations at the Patent and Trademark Office (PTO) and by making it easier to secure an injunction. The bill authorizes a third party to submit evidence to the PTO to oppose an application for a federal trademark registration. The bill establishes a procedure for any party to petition the PTO to expunge a registration for a trademark that has not been used in commerce. The bill also establishes a procedure for any party to petition the PTO to reexamine any trademark registration on such nonuse grounds. The PTO may also initiate such an expungement or reexamination proceeding. If a plaintiff has prevailed in court in asserting certain trademark rights, that plaintiff shall be entitled to a presumption that the plaintiff will suffer irreparable harm for purposes of determining whether the plaintiff is entitled to a permanent injunction. If a trademark plaintiff is seeking a preliminary injunction, that plaintiff is entitled to this presumption upon a court finding that the plaintiff is likely to succeed on the merits of the case. Under current law, a plaintiff must establish irreparable harm to secure an injunction. The Government Accountability Office shall report to Congress on PTO efforts to address false and inaccurate claims in trademark registrations and applications.