The door is "beaching" on what must be a slight rise in level in the tiled floor in the porch behind it, which coincides with the outside sweep of the door as it opens.
The bit of the (exterior)door that is now scuffing the tiles is actually a triangular-section timber nose that is attached across the bottom outside edge of the door to improve weathering. This has probably been in place since the house was built (c. 1905). The door is a large one compared to what's typical today, and it's heavy, so I want to take a millimetre or two off the area that's causing the problem, but I want to do it without removing the door.
Other than the obvious angle grinder, is there an easy way to do this?