I don't know what was really going on... I removed one song, got the "Normal" status. I removed some other files, got "modified". ReAdd the first file that was removed, got the "Normal" status again.
What I've decided to do is put my memory card in my MacBook Pro. I got an error that the card wasn't readable. My MacBook is supposed to support SDXC standard with and extFAT formated card... so it looks like that my card had a problem. I decided to reformat the card with FAT32 even if SDXC card are supposed to be extFAT. I put the card back into my phone. I synched all music files.... and I got the "normal" status again. I modified my playing list in iTunes... I synched again... status stil shown as "normal".
So I don't know what was the problem exactly... I suppose that the file system on the card was damaged in some way... but I really do not know what caused this problem at first.
Anyway it works fine now... so this is the most important thing.
Virgin Mobile Canada - Samsung Galaxy Note 3 SM-N900, Stock ROM