Do you connect light stability wires to ground nut?
That is a ground wire and should be connected to the equipment ground. If you have a metal junction box then it should also be pigtailed to the ground.

Since the fixture you have does not have a permanent mounting method and hangs by a hook, then it requires an external ground wire. Hence the bare wire.

Attaching it to the green screw is fine if you have a metal grounded box. If the box is plastic it should be wire-nutted to the bare or green equipment ground wire.

Good luck and be safe!