Try using a pencil eraser to wipe the tiles. This household trick is great for cleaning small sections of stained grout. Simply run the eraser of a number 2 pencil over the stain until it is gone. Use a clean white or pink eraser. Sandpaper or an abrasive grout tool may be more effective for stubborn surface stains.
Use baking soda. Make a paste with baking soda and water. Apply it to the dirty grout using an old toothbrush. Scrub the paste into the grout well. Wash the grout with warm water when you are finished. Most dirty grout can be brightened using this natural method. For the tougher stains, allow the paste to sit for a few minutes before you start scrubbing.
Use bleach to remove stains that are more difficult to remove on tiles. If natural methods don’t work, try a bleach solution. Mix a 75/25 solution of bleach and water if your grout is white. If the grout is colored, you will have to use plain water. Do not use bleach on colored grout as it may remove the coloring. Use a toothbrush or the edge of a sponge to clean the grout with the solution. Rinse the floor with warm water after you are done to remove all traces of bleach.
Be careful to not get the bleach solution on the tiles. While using the bleach, wear a pair of rubber gloves to protect your hands. After the floor is completely dry, carefully apply a coat of grout sealer to the grout between the tiles to prevent it from absorbing dirt in the future.
If you don’t like using bleach, you may be able to find a commercial grout cleaner that will be stronger than a natural cleaning product. However, check the label to make sure it doesn’t list bleach as an ingredient.