I always figured it was a play on words based on the stripe on the back of a credit card, the magnetic strip.
I was searching online for "stripe offline payment meaning -stripe.com" but overlooked "swiped (Magnetic stripe)" from linkedin content. Now it makes sense, that this kind of stripe is meant. My cards have a dummy stripe in that place, since the early 2000s I have not seen actual magnetic foil in that place on my cards in germany.