You don't have to remove any of this when replacing the battery but doing so will make the job easier and can prevent from accidentally knocking the adjacent cables.

I use a small screwdriver and pry underneath that brown bracket from the top edge by the camera (with the elongated metal cover removed of course) all the way before the battery, then lift up just enough for me to unhinged the battery out of the secure post. I don't know why Apple has to go through ALL THIS just to connect the battery since there is a small screw AND ADHESIVE securing it anyway. Nonetheless the whole job (replacing the lcd screen and battery was a major pain in the neck!

Not difficult at all to dismantle this thing. I do it all the time for maintenance.