The bills are stored in bundles held together with a paper strap. Many banks / tellers will stamp the strap with the bank or amount or teller I'd or what have you. The stamp will frequently partially land off of the strap and on the outside bill.
I agree with the others. When you see and understand how our paper money is packaged and distributed, it all makes sense. The paper banding around the pack protects the center, but often enough, some stamping ink makes it the edges of the band.
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