This is called the Agnostic Note because it does not have the words IN GOD WE TRUST printed anywhere on the note. The black mark along the right side is a shadow but the half inch long black line on the edge of the note above Washington’s head is a printed guideline for where to cut the note.
I guess the 1935 G I have is a "Pious Note?" The notes with the motto are less common than the ones without, but calling them "rare" seems like a stretch. A law passed in 1955 mandated the motto on all currency. The 1935 series was still being printed that late because the date on bills then apparently referred to the design rather than the printing date. This mandate also added the "under God" in the Pledge of Allegiance. A Porky Pig cartoon from the 1940s has him reciting the pledge without "under God." This note came to me from a deceased relative, who may have put it aside because of the motto's addition.
