On Enter means the macro is running before you have made your selection. It would be more logical to run it after the CC value has been changed.
Based on the name of your macro, perhaps you are not aware that it only works when it has the right name AND the code is placed in the
ThisDocument module.
Try this code
Code:
Private Sub Document_ContentControlOnExit(ByVal aCC As ContentControl, Cancel As Boolean)
If aCC.Title = "Awaiting Response" Then
If aCC.Checked = True Then
aCC.Range.Paragraphs(1).Range.Font.ColorIndex = wdRed
Else
aCC.Range.Paragraphs(1).Range.Font.ColorIndex = wdGreen
End If
End If
End Sub