That "hardware" is the spring isolators. Basically rubber bushings which go between the spring and axle/frame to quite the ride and stop metal to metal contact. They are held in by the spring. There don't appear to be any spring retaining brackets, so everything is held by spring compression force.
Supporting the axle with a jack, unbolting the shocks and lowering the axle usually drops it down far enough to remove the springs by hand. If they cannot be pulled by hand DO NOT try to pry them out. Use an internal spring compressor to compress the spring and remove it.
After removing the springs, check the isolators for holes, rub spots, or other damage. Replace if needed.