This simple procedure will clear your Time Machine settings, including the list of excluded items. The backups themselves won't be affected. If you have a long exclusion list that can't be recreated easily, you may prefer a more complicated procedure that preserves the list. In that case, ask for instructions. Otherwise, see below.
Triple-click anywhere in the line below on this page to select it:
/Library/Preferences/com.apple.TimeMachine.plist
Right-click or control-click the highlighted line and select
Services ▹ Reveal in Finder (or just Reveal)
from the contextual menu.* A Finder window should open with a file selected. Copy the file to the Desktop. Then move the original (not the copy) to the Trash. You'll be prompted for your administrator password.
Restart the computer and recreate your settings in the Time Machine preference pane. It will falsely show that you have no backups. Don't worry; your backups haven't been touched. Add only the USB drive as a destination—not the NAS, which is unsuitable for use with Time Machine, despite what the manufacturer says.
The next backup may take much longer than usual. If TM now performs as expected, delete the file you copied to the Desktop.
*If you don't see the contextual menu item, copy the selected text to the Clipboard by pressing the key combinationcommand-C. In the Finder, select
Go ▹ Go to Folder...
from the menu bar and paste into the box that opens by pressing command-V. You may not see what you pasted because a line break is included. Press return.