You did not say how deep the scratch is. I do not know if you have
access to a lapidary machine (grinder). Nor do I know how far the
stone (top) is above the surface of the mounting; it might be best if
you could take the stone out first, or may it won't matter if
careful. This article may be of some help in what is to be said next.
This could be done by hand, be advised that agate is one of the
hardest materials, so this will take some time. If you opt for
sanding get wet-dry, and get the kind suitable for auto body repair,
silicon carbide, and use wet. The incorrect choice may be the
problem, but of course this is a sand, sand, and sand thing, also. In
any event, either with a wheel (of a cabing unit) or sand paper,
start with a 100 to 150 grit, until you can not see the scratch, next
a 200-250 wheel (or sand paper), next a 600 sand (some go 400 then
600, not nessasay, but would mention it). At this point it should be
suitable to buffing with Cerium Oxide (the usual choice, tin oxide
would work, zam is useless for stone of this hardness). The
importance of the final fine sanding is the single most important
part of getting a high polish. There should no visible scratches at
all. If you see scratches, when beginning to polish or the surface is
not smooth go back to sanding.
Now what has been said has some caveats, now what has been said
applies to using silicon carbide grinding wheels, followed by, If you
are using silicon carbide, 600 grit sandpaper on a drum or disk. This
wears fast, it becomes finer grit (mixed, as breaking down in use),
and it is all you need for a pre-polish. (If using sandpaper, by
hand, you may want to go with 1200 next, after 600).
If doing this by hand, use a flat surface, maybe a sheet or two of
paper as pading, tape the sand paper to this surface, providing there
is good clearance between the mount and stone it may actually help to
leave it in, easier to hang onto while doing it.
If using diamond equipment (such as a Genie) just start with the
first wheel, the second etc., by the last it will be finely polished.
This can be done also with a faceting machine, use a course lap
until the scratch goes away, and a finer (medium, maybe 600) lap,
1200 diamond is a fine pre-polish for agate (polish) and of course
you can use a lap above 1200, maybe 30-50,000 to polish it.
It would be possible to use other equipment, flex shaft (orchid has
a step by step article on how to make a turquoise cab with a flex
shaft). Or for that mater, even a drill with the right sanding
disk(s) or drum(s), and a buffing wheel loaded with a polishing
compound, but as this is a flat top you will have to use care (much
more, with this smaller diameter equipment), to insure it stays that