I have only heard the last two meanings of this word.
grout
n.
5ME < OE grut, residue of malt liquor, fine meal, akin to greot, GRIT6
1 a) coarse meal b) [pl.] GROATS
2 [usually pl.] [Brit.] sediment; dregs
3 a thin mortar used to fill chinks, as between tiles
4 a fine plaster for finishing surfaces
vt.
to fill or finish with grout
grout$er
n.