The platform escapement is a horizontal platform straddling the front and back plates and attached by four screws. It was clearly visible with its oscillating balance wheel through the top glass before you removed the case.

Notice how an arbour and pinion descend below the platform. The pinion engages with the contrate wheel, the final wheel in the gear train.

If you can leave the screws in their screw holes, so much the better. It will make it easier to replace the platform escapement as these screws are quite small.