I'm assuming this is an external drive that you use for backup purposes.
The fact that you formatted it as MacOS Extended Journaled Case Sensitive itself should not be a problem. You should be able to make any copy (even with CCC) to a case-sensitive drive.
The problem you have encountered may be from name conflicts - some file(s) or folder(s) with names that differ only by the case of one or more letters in the name. (e.g. "File1" vs. "file1"). In that case you could either get an error or one of the files or folders simply won't be copied ... neither of which is desirable. In the case of iTunes this could happen if you change the name of a song, playlist, album title, etc. by changing a capital to lower case or vice-versa - this could result in a name conflict.
I'd suggest the best way out would be to back up any necessary data to another drive; then reformat this drive to Mac OS Extended Journaled (NOT case sensitive).