"why wouldn't he remove the garrote and take it with him, like the duct tape and stun gun?"

That's a good question. One of the hallmarks of a disorganized offender is to leave the murder weapons at the scene and on the body. In this instance, he left one. Was he being disorganized, or, did he pose the body in such a way to appear as if she were still alive, but once the blanket is pulled back, all hope is dashed?