It always looks nicer when the trim is applied after the tile.

I agree, i would remove it, apply the tile, grout then reinstall the trim piece over top for a clean look.

I agree, i would remove it, apply the tile, grout then reinstall the trim piece over top for a clean look.

Your trim would be easy to replace and look much cleaner to install new after the tile. I can't tell how old your windows are, but did run into a problem with my old ones. The wood under the sill was on a slope and had to add a strip of wood to mount correctly. Plus the center style couldn't be removed with two windows creating a large one. I would also remove the side trim and fit after the sill. Family Handyman has some great how tos for working with many types of windows.

If the casing is removed, the jambs would have to be built out the thickness of the tile and thinset before being reinstalled.

Original fabric of older homes should only be replaced under the most dire of circumstances, certainly not in this situation.