A spray cleaner with bleach.....and a tooth brush!
Linda C

Suggest you use the Mr. Clean Magic Eraser sponges. Did wonders on our DDs newly bought older home's bathroom grout

I'd definitely try Finazzle. I moved into a house about a year ago that had horribly dirty grout in the kitchen - what used to be white was black! Over the last year I'd tried scrubbing it with an industrial degreaser, bleach, ammonia (not with the bleach though;), and spic-n-span. At some point I'd bookmarked the site to order Finazzle after seeing it suggested on one of the message boards but had forgotten about it. I was cleaning the house in preparation for a party and remembered, so ordered it figuring it might be worth a try. It was wonderful! I don't know what it does with colored grout but it was great on white. It does take of the top layer of grout so you'd need to re-seal afterwards (I still need to do that) but it was worth every penny.

You could try the clorox bleach pens. They are gel bleach, so the product will stick there, as opposed to liquid bleach that lands there for a second then drip down and dries off.

Home Depot has a product called Tile Lab. There is one for cleaning and one for sealing. I have used the cleaning one on my gray grout and was very pleased. It was alot easier to use than Finazzle and not as expensive. I sprayed it on the entire tile, waited a few minutes then took a scrub brush and went over the tile and gout. Then mopped up the remaining solution. Home Depot is the only place that has it - Lowes doesn't.