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?