For certain repairs (e.g. hard drive), disconnecting the battery connector is not necessary but is recommended as it prevents any accidental shorting of electronics on the motherboard. If you do not disconnect the battery connector, please be careful as parts of the motherboard might be electrified.

Use the edge of a spudger to pry the battery connector upwards from its socket on the logic board.

It is useful to pry upward on both short sides of the connector to "walk" it out of its socket.