How do we determine how much the surface of the Earth deflects due to tidal forces from the Moon (and Sun)?
The Wikipedia article on Earth tides includes a table showing how much the crust moves in response to the tidal forces from the Moon. The maximum movement is a shade under 40cm, though more typical would be 10 - 20cm. Ocean tides can be up to 10m, though 4m would be a more reasonable value, so the movement of the crust is about one tenth that of the sea rather than one hundredth.
I'm afraid I don't know how such small movements in the crust are measured. I assume some form of surveying is used.