Deleted Folders from C Drive - Remain in Backup on External Drive

All backup programs work in a similar way.

You might want to research for a synchronization software.

The files will be updated according to the settings you have. Smartware allows you to keep a number of changes of the files. After that amount set has been backed up the oldest file will be discarded when a new change is made thus keeping the amount of copies of the files to the set numbers previously selected.