As far as I have noticed, management has no jurisdiction on what you install inside your unit, as long as it does not change the external façade of the building. Imagine management specifying what type of curtains you can install, or what colour to paint your rooms.

They can however ask you to change the front door grille, as it leads to a common area. This is usually the only grille they have jurisdiction over.

You also should not need to allow access into your unit. Ask for your deposit back, and tell them to inspect the surrounding area for compliance (no trash, clean, no damages, etc) to the permit you applied for. Unfortunately there are a lot of little Napoleons around, and you may have to escalate this issue to the Commissioner of Buildings for final resolution.