Don't pry against the battery during this step. Angle your spudger under the left or right edges of the press connector.

Use the flat end of a spudger to pry up and disconnect the flip battery press connector.

To re-attach press connectors like this one, carefully align and press down on one side until it clicks into place, then repeat on the other side. Don't press down in the middle. If the connector is misaligned, the pins can bend and cause permanent damage.