My very first Mappy speedrun got copyright claimed by JVCKENWOOD Victor Entertainment Corp. because of the mappy level music. Is anyone having the same problem ?

Yes, but a claim is not a strike, the channels are fine. It's just that you can't monetize that video.

Ok but can I mute or replace the music ? Is that going to make my run invalid by the moderators ?

If there is such a necessity, you can submit run without music from the game and it will be accepeted, however it's always adviced to have one. In this case, I would recommend to leave it, since, as Mingura mentioned, copyright claim pose no threat of video being deleted. Unfortuntately, it happens often for some games, for instance, few of my almost 4 years old Contra and Little Mermaid PBs on YT got immediatelly claimed and they are still untouched there. Besides, not sure, how YT works in every country, but you rather wouldn't earn anything before getting thousands of unqiue views.