I think you will need to speak to the installer and see what was used to adhere the marble to the wall those spots don't seem to have any sort of pattern that might be an issue with the material used to adhere the stone..

Those look like silicone fingerprints, not bleed from the back. Hit 'em with some acetone again and again; you may get lucky.

I agree with Pat. It's possible the product used for adhesive has migrated through the stone.

Woah. I just looked at the picture again and realized that's a wall, not a backsplash. That's adhesive bleed and there's probably no fixin' it. Expect more.