A lot of media and news services file false claims against videos they don’t like, breaking the fair use laws. What to do is to file a claim against them. The following text is from the copyright law of the US to put in the claim against them.
Copyright Act of 1976, 17 U.S.C. TITLE 17 . CHAPTER 1, 107. Limitations on exclusive rights: Fair use. Notwithstanding the provisions of sections 106 and 106A, the fair use of a copyrighted work, including such use by reproduction in copies or phonorecords or by any other means specified by that section, for purposes such as criticism, comment, news reporting, teaching (including multiple copies for classroom use), scholarship, or research, is not an infringement of copyright.
This shows that their claim against your video is false once you are not using it to profit from it but use in a legitimate use.