Magic Eraser works nicely to clean grout on a tiled countertop. First clean dirt and any residual grease off the tile (to degrease, spray the tile with vinegar; wipe clean and dry). Then scrub the grout lines with a dampened Magic Eraser. Finally, wipe away residue rubbed off the eraser.
To clean black mold off tile in a tub or shower surround, put some chlorine bleach in a clean spray bottle (be sure no residue of any detergent remains in the bottle!). Clean soap residue off the tiles as best as possible (vinegar will help with this, but if it’s very thick you probably will have to scrub it off with scouring powder), and then be sure all cleaning product is thoroughly rinsed away. If the bathroom has a window, open it; turn on the exhaust fan. Then spray the grout with bleach. Let it stand for some time. You may have to spray badly mildewed areas more than once to fade the black out. Use chlorine bleach only on white, as it may fade colored grout. Rinse thoroughly and dry after use.
It’s also possible to use oxygen bleach (the stuff that’s pitched as “color-safe” in the grocery store’s laundry section). ? It must be mixed with hot water to work. Combine oxygen bleach with very warm or hot tap water in a spray bottle (not so hot as to burn yourself) and apply liberally to mildewed areas. Oxygen bleach is said to be safer for colored grout, and it emits fewer noxious fumes.
To discourage regrowth of mold on tile and grout, leave the shower door or curtain open after showering. If possible, open the window after showering. Train users to wipe the tilework dry after showering. A squeegee or a microfiber cloth (hung over the top of the shower frame or curtain rod to keep it dry) works well to remove water and soap, and if used regularly minimizes bathroom cleaning labor.
It is important to avoid deposits of soap scum, hard water, and mildew by cleaning and drying the surface after EVERY shower. Once hard-water soap scum has built up, it’s difficult even for professionals to remove.