Whatzit? Name this dryer or washer thing-a-ma-bob
That may very well be a washer tub restraint device. The tub in a washer machine is often mounted in a way that takes up vibration during normal operation. During shipping from the factory additional items are added to the washer to restrain motion in the tub to prevent knocking around and/or damage. This cable hook device could be one of those restraint devices.

If a local delivery service brought the washer to your house they very often remove the restraint devices and other shipment items. This could include tapes that hold doors shut, ties that bind up wires, tub restraints.....it could be that the service people didn't extract all devices.