Use angled tweezers or an iPod opening tool to slide up the brown connector latch, holding the orange battery ribbon cable in place. Make sure you pull from both sides of the latch. You only need to lift the brown connector latch up about 1-2mm to free the cable. Do not lift more or remove the latch, or you might pull the white connector with it!

Don't lift up too far or you could pull the battery connector out of the logic board.

Make sure to slide the brown connector directly upwards. The connector is frail and will break if it is accidentally shifted to the side. The connector has hooks at the bottom to hold the cable in place. As soon as you break one of the arms you will have problems putting the battery cable back on. If it breaks put the cable in the slot and then push the brown holder in place to keep the cable from slipping out.

Remove the cable from the connector.