You see that line, instead of the usual button, whenever one of your own drivers is holding the order and the next step would be shipped or delivered. Those two steps belong to him: he taps picked up when the parcel is in his hands and delivered when it reaches the customer.
Everything else stays yours. Marking the order ready is still your button, because that is the cue his app waits for before pickup unlocks. Collecting the cash is still your button too.
If you really do need to move the order by hand, cancel the delivery on the order's Delivery card. The order itself is untouched, the manual button comes back, and you can dispatch a driver again later.