They are increasing the precision of the phase while decreasing the precision of the amplitude. Since the amplitude of the light determines how hard it pushes o

They are increasing the precision of the phase while decreasing the precision of the amplitude. Since the amplitude of the light determines how hard it pushes on the mirrors, this has the side-effect of also making the positions of the mirrors more uncertain. To get the most accurate measurement possible, I'd guess that they would squeeze the light until getting any additional precision in the phase was not worth the added noise in mirror position.