There is no relation.
Time Machine backups : my opinion is that this is a real waste of disk space, usefull for a few number of files but that's all ! In case of a reinstallation, everyone is performing a fresh installation ... In addition, after a certain time, TM erases the oldest files.
I personnaly backup only on mediums (CDs, DVDs, DVDs) etc ... then i'm always sure to find again what i'm searching for.
iTunes : a "!" means that you have moved from one place to another an audio file (or erasing it by error) and iTunes has just stored a link to the file and not the file inside its own folders. Probably you have never consolidated you library. The question is : where are you storing your files ? inside your mac plus inside external drives ? Please make sure, if you are managing often files in iTunes, to consolidate them in order for iTunes to copy them inside its own folders, else it becomes quickly a nightmare.
iTunes manages files on 3 different ways now :
- real files inside it
- links to files out of its folders
- files from iTunesMatch