Removing grout that is adhered to a tile floor can be difficult. The type of tile greatly affects the difficulty of grout removal. Also, if the grout was polymer-modified, it may be more difficult to remove.
In general, the more porous the surface, the better grout will adhere. Conversely, grout is more easily removed from dense impervious tiles (e.g. porcelain).
To remove the grout, start with an alkaline cleaner and a nylon scrub pad. Make sure to check that the scrub pad is not damaging the tile. Normal floor tiles will not be affected by using a scrub pad, but some decorative tiles do not have the same surface hardness. It is best to check your decorative in a secluded area.
If the scrub pad is not effective, there are specialty cleaners on the market that chemically attack the grout. Typically these are weak acids. As with all acids, follow the manufacturer's warnings carefully and use caution. Always check the tile in an inconspicuous spot first in case the cleaner affects the tile.
Again, these specialty cleaners will not affect most floor tiles; yet, it is prudent to check.
Some tile installers use stronger acids that they carefully dilute. While experienced professionals can do this, there are great risks in doing so. There is the possibility of bodily harm as well as damage to the surroundings.