My mouse says it's holding something, and the option to recycle comes up, but the punched card is invisible so we can't really use it. I would love to include a screenshot but there's nothing to screenshot
Update: When you pick the card, it sets its initial height to the *ground floor* regardless of which floor the camera is actually viewing. So it was just underneath the building. Viewing the ground floor, picking the card, and moving the camera up works