Ben wrote:
The front door in my house leads to a small tile landing. There is a
space between the threshold and the tiles, which I believe was filled
with grout when the floor was installed. Should I refill this with
grout, or something else?

I would try to find a silicon grout that matches your sanded grout as they
are more forgiving when separated my two different materials. I have no
personal experience with them but have seen them used on home improvement
show where a tile mosaic met up with a hard wood floor. They apparently have
the same colour sand in them and look very much the same as the sanded
grout.

I have been in my house for 2 and 1/2 years and still have not filled a few
spots on the edges of my door frames where the previous owner tiled around
the door frames instead of cutting them off and tiling under them. I have
been meaning to look for the very same product for this job.