An auto scrubber with a brush would have been the way to go.
If you were using a really hard scraper then you may very well have gotten into the grout.
Since it was as dirty as it was I would have used a light acid solution.By acid I am not talking about muratic acid!No way.
I'm talking about a brick and tile cleaner that you can purchase at tile stores.Typically a brick and tile cleaner is used for new construction as it
removes light grout and grout residue from the face of newly installed ceramic or porcelain tile,but I discovered that it also is great for just
cleaning up grime on the same types of surfaces.
I am certain that you will get people saying to use a degreaser which will also be beneficial.Experience
is what makes us differ in our
methods.At times there is more than one right answer, it just depends on what you become familiar with using.
Doing it by hand istorture.An auto scrubber with a brush assembly.You may be able to rent one from someone.