Removing construction debris from a carpet

I had a lot of conustrction going on it a stairway where all the old plasterwork was taken down and the new plasterboards put up. This has left a lot of stains in the carpet. I have a proper vacuum with a carpet attachment, but it does not remove anything.

I also rented a Karcher carpet cleaning, a Puzzi 8/1. I cant see in the tank that it picks up a lot of junk, but it still does not look cleaner. Is it possible to recover the carpet at this stage?

I have yet not tried any products.