How to clean old, dirty grout without damaging marble tiles

Q: The white polished tile in my entrance hallway and half bath has grout between the tiles. It probably has never been cleaned. When I recently had my carpets washed, I asked what the company could do to clean the grout. I was informed that any product would harm or ruin the marble tiles. The now-gray grout is so ugly. Do you have any advice?
College Park
A: Acidic cleaners damage polished marble tile as well as grout, so stay away from those. However, mildly alkaline cleaners can be used for both materials. These include Spic and Span and Mr. Clean. To be sure a product is suitable, check the label or search the Web for the product name and the word “marble.”
Be sure to rinse thoroughly, or the cleaner may leave a sticky residue. The easiest way to do that? Use a shop vacuum to remove the soapy water. Then wipe the floor with clear water and vacuum up any residue. Rinse at least one more time.
Once the grout and floor are clean, apply a penetrating sealer to the grout — and to the stone tiles if they aren’t already sealed. To test, sprinkle on some water. If the water beads up, the tile and/or grout are sealed; if the water sinks into either material, it is not sealed or is in need of resealing. Miracle Sealants’ 511 Impregnator Sealer ($34 for a quart at Lowe’s) is an example of a penetrating sealer suitable for marble and grout.