Your tile?
My guess is that the grout is actually that white color but it could be the cleaner you're using. Is this tile on your shower wall, or on a floor? Is the tile greasy and what degreaser are you using?
The degreaser is the chemical that worries me. If its shower tile thats covered in soap scum I would get a good coating of Lysol Bathroom or Tilex Bathhroom soap scum remover on their, letting the product sit for about 10 minutes. Use an SOS green scrubby sponge with a multi purpose disinfecting solution in bottom of tub and wipe down down walls. Its important to let the chemicals do the work for you.
For a tile floor I have a 5 step process that I use every once in a while as needed for tile restoration:
1) Vacuum floor with bristled bare floor brush
2) Thoroughly wet mop floors with good cleaner and ensure they are very wet. Armstrong floor cleaner works very well, Mr. Clean or other professional tile cleaner works good. I'm not a fan of Pine Sol.
3) Soft Scrub cleanser and a good comfortable scrub brush. Lemon or Orange formula are best. DO NOT use a a gel or bleach based cleanser. Liquid regular soft scrub is the best. The thorough wet premopping with Armstrong has already started softening the dirt. Apply directly to floor Soft Scrub entire length of grout lines. Results are instantaneous.
4) Rinse-- attach floor squeegee to Hoover Steamvac with plain water only in clean water tank. Just like shampooing a carpet. Use the spinscrub, dispense water and suction up solution.
5) Wet mop floors with water only. This is the last final clean step to ensure all loose dirt and cleanser is removed for a nice finish. I highly recommend a rectangular shape with automatic ringer sponge mop. The automatic wringer isn't really automatic, but its the one up on the handle not down by sponge. The Libman gator works very well or Quickie automatic/ Clean Results from Lowes, or HomePro line. Since this is the final mopping, work to wring out mop thoroughly to absorb all liquid for a faster dry but gorgeous finish.
This sounds hard, its really not, it's great exercise, very rewarding and your floors will look new again!! I've been cleaning houses for years and this is my proven method. You can try a long handled deckbrush but you'll achieve much better results from hands and knees with a standard scrub brush. The compact, long ways design of a typical bathroom scrub brush means with each stroke you get much more contact with the surface and the brush better conforms to the grout line.
