You should use the same kind of material as the original installation.
It may not be grout, which is basically concrete. It may be a good
grade of silicone (not just latex) caulk.
Make sure the surfaces on both sides of the gap are exactly level. If
not, you will need to make them level by shimming.
The installation is about 11 yeas old so I have no idea what was
originally used. It is not a flexible caulk of any kind. The pieces
that I am pulling out have broken and a quite hard.