Use a spudger to carefully pry the battery connector up and disconnect it from the logic board.

In models that don't have a removable black spacer, you may need more clearance to unplug the battery connector from the logic board. Remove the screw at the middle of the left I/O frame, then lift up the lower end of the I/O frame. If removing this screw doesn't give you enough clearance, remove the I/O frame.

Look at the pinout on the bottom of the battery connector circuit board. If there's no gap in the two rows of pins (if both rows contain ten pins), it's the Non-Energy Star version. If there is a gap (two rows of six pins each, separated from two rows of three pins each), then it's the Energy Star version. These two versions aren't interchangeable.

When reinstalling/replacing the battery connector, make sure to route its short black cable into the channel provided for it in the lower case frame, or else it might press upward on the left edge of the top case at this location, preventing the top case from laying flat here.