Why is a ground wire of this outlet wrapped around the bare portion of a neutral wire at this outlet? This ground wire is a pigtail that is joined with the two other ground wires in the box.
This outlet is controlled by a switch. There are additional outlets after this one. I have checked several other outlets in the house and do not see this repeated on those.
I am going to replace the outlet. Should I unwrap this ground wire? 
The neutral wire is broken somewhere and that is a bad cheap lazy hack to have that outlet work.
If you remove the ground from that wire and that outlet keeps working and everything else on that circuit keeps working, then someone just wrapped that ground around for nothing. Ground and neutral should only connect in the main panel and nowhere else.
Turn off the breaker for that circuit before playing with the wires.
Since you seem to have aluminum wires invest in a torque screwdriver and make sure all connections are tighten to specific torque.
