Use a pair of angled tweezers to firmly grip the battery connector and slide it straight out of its socket.

If you're having trouble, gently rock the connector side-to-side to help loosen it.

During reassembly:

Insert the connector into its socket so the side with raised plastic in the center is facing up.

Push on the edges of the connector with the flat end of a spudger until it's fully seated in the socket.