I use a product called Bring It On Cleaner. Works like a charm. I even used it to clean burnt food from a pot I left on the stove.
What's The Fastest Way To Clean The Soap Scum Off The Bathroom Shower?
Try using non-abrasive comet with bleach and a non-scratch scrub pad or use baking soda and vinegar with a non-scratch scrub pad. Make sure to use hot water it helps dissolve the dirt and scum better than cold water.
Turtle wax takes off the scum fast and also puts a nice white coating on the grout, two problems solved at once.