Finishing old grout?

My daughter is about to move into her first house, the previous owners had tenants, and I suspect that as part of tidying the house up for sale, they have fitted "mosaic" sized tiles in the kitchen, but the grouting is awful.
In places it looks as if they forgot to polish off the excess grout, and it has dried and is of course rough on the tiles.
Is it possible to remove/polish this dried grout, as it should have been when it was applied?
A damp cloth may not hack it, can I use some sort of power tool/drill attachment to save on the elbow grease?