Agree 100%. LVP with a straight urethane finish is relatively soft (Around a 2 on the MOH's scale) compared to a urethane that's modified with ceramic bead, aluminum oxide, or synthetic diamond dust (7-10 on a MOH's scale respectively).
Also, not sure what the scope of your project was but if it involved dry wall dust at all this is probably one of the hardest things to clean off a dry floor with any amount of texturing with no adhesive residue. With the tape residue it's going to be a lot harder. It generally requires a lot of rinse and repeat so don't be surprised if you have to do multiple cleanings to get the problem resolved. It's just such a fine dust that when it gets down into the texture of the product it's a complete pain in the rear. Be patient and you will eventually get it but just go in with the mind set it's not going to be a one-time cleaning. It's probably going to take multiple.
As a last resort you may be able to rent a small auto-scrubber from a local janitorial supply. I would try to clean it by hand first though. If you go this route, use microfiber pads or the new "Astro turf" pads. The big advantage with the machine is that it's going to put down the cleaning solution, agitate the dust, and then suck the dirty solution back up (Hopefully with the dust). The downside is it's putting down a lot of water to do that. They are really intended more for cleaning commercial floors where we are typically over a concrete slab.
Lastly, for what it's worth, the flooring should ALWAYS be the last thing to go in on the project for this very reason. A new floor should not be exposed to paint splatters, drywall dust, saw dust, dirt and miscellaneous debris from construction. I only mention this because if the GC was responsible for the timing and management of the job in the contract then you might be able to make a case for them to have the floors cleaned professionally.