Re: Door Trim OVER Tile?
You can either fire up the dry diamond cutoff wheel in your angle grinder and trim the tile back, or get out your router and (trim-thickness permitting) make a recess in the back side of the casing to house the tile. Shimming out the rest of the casing perimeter would work, but be a kluge, as it would be obviously thicker than the rest of the casings in the room/house.
Always nicer to tile up to the casings with neat cuts, leaving the small gap for grout-color caulk.
Remove not the ancient landmark, which your fathers have set.