Use a spudger or your fingernail to pry up the edge of the battery connector resting against the flat clip enough that the whole connector pops out of the clips securing it.

During reassembly, place one edge of the battery connector under the large upper clip, then press down on the opposite edge to fully seat it.

Make sure the battery connector is oriented correctly. The wider part of the battery connector should fit between the left and right flat lower clips.