klaraspchr I'm not sure why the table disappeared, but you can unblock the spot it was sitting although you'll have to refurnish the entire house when you move the household back in. Just move out and keep the furniture. All objects in the house end up in the household inventory. The invisible object will either become visible again or it will still show as invisible, but you can easily identify it and delete/sell it from the inventory. One thing to keep in mind is that you need to empty all containers like storage chests, flower workstation, fridge, DU chests, butterflies in the display case, any books you purchased in bookcases, marbles in the jar, etc., before you move out. I suggest you collect all collectibles on display or hung on walls, so you don't lose credit in the collections panel.
Edit: Gagea25 and I must have been responding at the same time. Her suggestion is probably easier and will be less work to get rid of the invisible object. If it doesn't work, then try moving out.
Hope this helps.