Sources tell TMZ ... Love caught wind of the tune -- which was uploaded to YouTube last week -- and with the help of a real Nirvana member ... confirmed it was fake. Courtney is part owner of Cobain's music rights, and got YouTube to take down the song.
The people behind the fake jam claimed to have hacked Love's computer to uncover a rare track ... which Cobain never planned to release. We're told that whole story is also fake -- Courtney never had the song ... nor was she ever hacked.
Still, her lawyer Richard Dongell tells us Love is pissed off enough about the phony recording that she's working with law enforcement to track down the impostor.