I put two irises.

One is before the half wave plate and along the squeezing path.(Shown in the attached figure 1 and 2) As you can see this iris equips with a rotateable blocker. We chould also use this block or unblock the beam.

The other is just before homodyne's BS along the LO path.(Fig 3)

I also put a black wall to block scattering lignt.(Fig 4)