Dremel.

No. Grout will not change the color of the tile

Is this a shower floor?

. No way does color bleed from a ceramic tile. The specks in the grout look like a bit of grunge was mixed in with grout, call the tiler back. And what was the prep BEHIND the feature wall? Only the installer is going to able to help you here

this is the feature wall and the photo above is a close up. In person the grout marks look like ants on the wall

Perhaps in those spots, the dots were a bit thicker and the grout not holding there. May be with a grout colorant pen you could dab color on them to cover them up.

I can see that the dots bleeding through are exactly in the middle of each side of the hexagon.

oh dear, that is a problem. I hope they can remedy this for you easily, I feel your pain!

Did this issue get resolved? If so, would you share how it was? Thank you!