It depend! however, it has the same mechanism throughout the game. I will try to explain to you.
look at my house. I have a bench, a tree and flowers here. these items can't be moved when we meet them on Tibia's map (example in parks, cities), so they can't removed in houses too. It's the same with the dustbin, any counter or lamps.
Differently in the case of furniture that we can push. For example this furnitures in your pics or these (Harbour Lane 3, Carlin original after win auction). You can move these items on the floor, so you can remove them.