The problem with covers is that you do not own the song, and most likely do not have permission to use it - thus the copyright claim. There is really nothing you can do about it (short of paying licensing fees). I run into the same thing when I film outside. There is always some karaoke around (even just in the background), and it flags the copyright
(the Philippines is a noisy country). I have learned to shoot/edit around the songs. Of course that would not work if my goal was covers...