The court will have 1 or 2 hearings on your Motion to Impound.
The 1st hearing may take place on the same day you file the motion, before the other side knows you filed it. The court calls this an "ex-parte hearing."
If you get a hearing on the same day and the other person is not there, the court may schedule a 2nd hearing about 10 days later. At the 2nd hearing the person on the other side of your case gets a chance to object to your motion, and explain why the court should not impound information.
All hearings on family matters and restraining orders are open to the public and recorded. This includes hearings on Motions to Impound. In some extraordinary circumstances you can ask the judge to “close the courtroom” for the Motion to Impound hearing – then, only people who are a part of your case can be in the courtroom. See Hearings in Probate and Family Court are open to the public and recorded