I think if it were me I'd get an oak threshold at
HD. They're only 5/8". Then cut off one bevel
and do a slight bevel or round-over on that edge,
which will then meet the tile.
When that's butted up to the tile it's only a 3/8"
rise. That may be too much for your mother, but
it's the only thing I can think of that won't look
tacky. Anything thinner in wood would risk cracking,
and while metal might deal with the slope it will
look a bit institutional.

| Thanks. I'll drop by Lowe's and HD later today when I'm out and about and
| see what they have. All I've noticed before has been wood which was thick
| enough to go over both surfaces making it an even larger hazard. I had
been
| leaning toward a shop-made tapered wood strip (I do have a full
woodworking
| shop) but I'm always up for an easy quick solution that does the job.