Separate the white upper plastic piece from the lower grey plastic base using a sharp screwdriver to get between the two layers. There will be some worrying cracking noise as the plastic clips come free and the parts separate.

Do it slowly, watch what is happening and carefully separate all around the remote. As you can see in the second picture, there will be damage to the edges as they are separated, but this is covered up by the battery lid when it is pushed back in place.