According to tile and grout cleaning Perth based experts, a cost-effective and safe solution is to make your own grout stain remover. Use a bucket to mix up one part bleach and one part baking soda. Apply this paste onto the grout and let it sit for a couple of minutes. Then use a grout brush, or even an old toothbrush, to scrub the grout. Use warm water to rinse the area afterwards.
After having a look at your photos in depth.
We would advise using LTP Grout Stain Remover diluted 1:5 parts water.
Apply in small workable areas, and agitate straight after applying and rinse with plenty of water. This will remove the staining.
Use Neat if staining remains after diluted application.
We would recommend sealing with LTP Mattstone H20 after once dry (24hours).