Certain items in rooms can't be removed.
Parlour: Curtains unable. All others ok
Kitchen: Shelves unable. All others ok
Dining: Benches on fireplace side and curtains unable. All others ok
Garden: Portals unable. Haven't tried anything else there.
This is all I've ran into so far as I just started training the skill. I did notice that all of the items that can't be removed are also the lowest grade item built.