So we don't know what type of grout it is yet?
I guess if someone who knew what type of grout is told you to use the Banish stuff, it must be a portland type grout.
Everyone seems to get their panties all bunched up when I suggest this, but here goes:
Get yourself some muriatic acid.
In a small container, put in a cup of water and add about an ounce of the muriatic acid. Don't put in the acid and then add the water.
Now get a bucket of water and two sponges.
First, wet down a small area with the water, using a sponge.
Next, sponge on the acid solution and use any of the following to scrub with:
stiff nylon scrub brush
3m scratch pad
razor scraper
grout removal tool (triangle head)
Sponge it on in a small area, wait 10 seconds, then start working. It may fizz a bit when it comes in contact with a dirty section of tile. As you are working, keep the area wet.
You can strengthen your solution by adding another ounce of muriatic acid.
When you have cleaned the section, rinse off the acid by sponging it with clean water a few times.