The usual way would be to send a DMCA takedown request to Apple, then if Apple doesn't remove the music you can sue Apple and the publisher of the music, or if the publisher of the music sends a DMCA counter notice and Apple puts the music back into the store, you can then sue the publisher.
Without a DMCA notice sent, they will have a hard time suing Apple successfully. If a DMCA notice was sent and Apple ignored it, then Apple is on the hook for damages. We'll see which one it is.
That would be a good start but in the end it might be messier than that. We would have to look at exactly where these recordings are being listed, the age and relevant copyright laws, the paperwork with the record labels etc. if Apple get a take down notice they go back to all of that and their lawyers decide if they are in the clear or not. So they could leave it up believing they have a good faith agreement with a label based on their paperwork and various laws when the label didn’t have a good faith agreement to enter into such agreements with the copyright holders.