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.

With a small screwdriver, loosen the screws until you can lift the platform off.

The platform escapement is delicate. Put it aside somewhere save when you remove it and don't attempt to disassemble it - that's a job for a watchmaker!

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.