Insert a thin tool (such as one of your tweezer tips) under the red and black battery wires, and slide it underneath the battery connector.

Gently pry straight up to disconnect the battery.

Pry only from the side where the wires attach to the connector—if you pry anywhere else, you may break the socket.

During reassembly, align the connector in its socket with the exposed copper wire facing up, and then press straight down to reconnect it, wiggling slightly as you press to help it seat correctly.