My suggestion is first talk to the builder to see what instructions he gave the tiler as i'm sure he doesn't want a dissatisfied client. Most tilers will check with the builder before grouting especially when a colour is not specified in a contract. I would then ask if the grout could be replaced, from the looks of it it will only be a couple of hours work. There is nothing worse than having to look at something you are not happy with. I would not use the paint product as it will alway look like it is covering a mistake. White will look better. Make sure the mixer body is waterproofed or you will have a leak in your wall, the membrane should lap onto the body from the wall if it is done well. All the best.

Ouch! redoing the job means scraping out the old grout and replacing. In my limited experience tilers hate doing this and may miss bits, I don't think the grout is as solid afterward either, ok on walls not so good on busy floors. If the grout hasn't been sealed and given that it is so absorbent anyway it should be simple to recolour, just test first as it may change colour when it dries. Then use a quality tile and grout sealer, worth the time imho. I would hesitate to tell a professional tiler which brand of grout to use unless you have experience, they differ in quality, colour is up to you of course.

What a beautiful tile! Rule of the tump - always match the grout to the tile. Specially with such a strong patterned tile, otherwise the grout also becomes a clashing pattern. I'd pick light grey to avoid pure white cleaning issues. I have these type of tiles in my patio, you will have to be seal them with penetrating sealer after installation, but other then that you will love them forever

Lots of good ideas here. If you do have a carpet remnant overstitched along edges, be sure to specify the thread is to MATCH the colour of carpet. I know this sounds like a no-brainer, BUT we had long and wide carpet runners made up, colour was dark brown. When we unrolled them, low and behold the overstivhers had used WHITE thread. We were stupefied. Who knew one must specify the obvious! Anyway, hubby had a brilliant idea: he used black magic marker and carefully coloured over the white. You would never know it had ever been anything but!