Thanks, davidro1, for your advice. I bought a handheld steam cleaner and the grout in shower and kitchen look like new again.

This is one of the most pleasing posts, to me. After six weeks of you took the time to find the thread and post. Thank you!

And I'm glad to hear that a steam cleaner does a great job. We haven't even completed our reno yet and I'm starting to stress about how I'll be able to keep it looking like new!

Thanks!

Wow I'm sold I too have a marble floor in shower and I have been using dollar store bathroom spray cleaner cause nothing got rid of the pink mold in the grout. So I would spray, scrub, and wash off quickly. But I might have to do this several times - pain! SOLD!

annemouse, which handheld steamer did you buy? I use a steam mop on my tiled floors and it works wonderfully on the tiles and somewhat on the grout but it's not a deep grout cleaning that my 10 year old kitchen grout needs. Steam and alcohol are my two favorite cleaners :)
Monica

We spray off our shower walls and tile after each use with clear cold water and and squeege, too. So there was no real soap scum to deal with and the shower looked fine from a distance. But after the shower was in use for half a year or so that pinkish algae started to build up on the grout and the best way to remove that without using bleach was the Magic Eraser. But I was hesistant to use that too rigorous or often because it is somewhat abrasive. Also, that pink algae came back each time after a week or so.
After davidro1's recommendation to go for steam I ordered the Steamfast Sidekick Portable Steam Cleaner from Costco. First, I used it with the steam nozzle only. The pink stuff vanished, but was not totally gone. Then, I used the the softer nylon brush attachement which took care of everything. All in all I guess I spent about half an hour cleaning the shower floor grout lines (many, because we have basketweave). But that was worth it, because even after a month the pinkish stuff has not returned yet.
For the kitchen grout lines I also used the nylon brush attachement, but needed some dishwashing liquid on the oily stains that I could not get rid off using the Magic Eraser or anything else including bleach so far.

Just be careful and don't do what I did. I used the steamer on all the "grout" around the tub and realized after it had essentially melted what I had just steamed that I had confused grout and caulk.

Do not use a steamer on caulk. You will destroy it in record time.

So if you WANT to get rid of the caulk on the nasty shower doors (where the mold has grown underneath the caulk and you can't get it out), then the steamer might be a good idea??