We get many phone calls for help on this topic. You can do this yourself when you know the basics!
What is the pink or orange grime? This my tile friends is soap scum, and shampoo that is clinging to your grout. Step 1 is to take an aggressive Scrub brush, and use a pH balanced cleaner and some elbow grease to remove.
There are many DIY tools available, such as this Dremel Grout removing tool that will remove 1/16” and larger to prepare for new grout.
Dremel too for Multimax
3. Stain and Seal. You can easily use an acrylic off the shelf stain and seal to recolor your grout joints, to any grout color. All though the work is a little tedious, it is an instant change! Pro Tip: use nail polish remover if you get the stain on the tile to remove, and you can use it for chipped tile as a color fix. Lasts up to 15 years, here is a link on Amazon for a great product.