we had our bathroom remodel about 1 1/2 yrs ago

Yeah, improperly constructed. The mold goes all the way behind the tile. Maybe into the wall cavity too.

oH No :(! How can you tell this was improperly constructed? Is there anyway I can get rid of the mold?

Oh geez. I live in coastal FL, land of mold & mildew, in an old house with lots of tile. Mold is a constant battle here. We just use chlorine bleach on mold. I use strips of cotton on the joints, saturated w/ slightly diluted bleach and leave in place for an hour or more, then rinse well. A grout brush is a good minimal investment too. You can apply small amounts of diluted bleach w/ a squirt bottle and scrub w/ the grout brush, then rinse. Just make to ventilate; chlorine fumes are not nice.

Have you tried using Clorox spray cleaner with bleach and a good stiff brush? I would sure give that a try then leave the shower door partially open to help it shower dry faster and hopefully prevent this problem. Closed up damp showers will mold in no time at all.

you don't have a mold problem,you have a water leak problem.

I am not a professional but have built, waterproofed, and tiled my own shower based on expert advice from this site and from local tile stores. When I look at your in progress picture, I see no waterproofing between the tiles and the wall or even in the pan. It looks like they tiled right onto the substrate (hardiebacker?). I would expect to see Kerdi (pale orange sheets) or a roll on waterproofing product like Redguard (bright red) or Hydroban (green).

When a shower lacks a waterproof barrier behind the tile, over time water will get back there. Then once water is behind the walls or under the shower pan, it stays wet and creates the perfect environment for mold. I had an old shower (built in the 1970s) which eventually started leaking behind / under the tile. We did not realize there was a problem except that the shower simply would not stay clean. Eventually the failure was so bad that the floor became soft. When we tore everything out there was a significant amount of mold behind and serious damage to the wall framing and the plywood subfloor. It was a huge amount of work to repair all of the damage. I just wish we would have addressed it earlier.

Good luck!

FWIW, when I commented, the construction pix weren't there - not sure why...?

Now that I can see them, it does look like it may be more than just a moldy grout problem.

We have similar issues, to the OP, did you get this resolve?
Is this truly a grout issues or a water leak issues?