Restoring purchased music from CD on iPhone after iOS update

I have a CD that I purchased a few years ago, and I also copied the purchased music to my phone (as I do not generally use a CD player). It had been automatically deleted from the phone before, along with other purchased music that was not from CDs at that time. It will not allow me to move them from my laptop directory backup to the phone.

So, it appears like Itunes thinks it is not really purchased music and is not allowing me to put it back on my IPhone. How can I workaround this? Do I need to delete the files and copy them from the CD again, or is there another way? Please advise.

[Re-Titled by Moderator]