Whole milk is the first ink-remover to try. It has to be whole milk.
Cream or half and half might work, I never tried it, but you need the fat content to cut the ink.
Then patience and very gentle blotting.
Saturate the stain, blot, repeat.
Use a white cloth so you can see if you are lifting the ink.
If you can get it back to a faint gray, then put Stain-Sorb on it.
You get Stain-Sorb from Service Master or Merry Maids, a national cleaning service.
If they are not in your area try a mixture of baking soda and corn starch.
There are a lot of natural stain removal tips online that recommend both of those for stain removal.
I am just guessing that those are the two products in the Stain-Sorb.
You pack it on top of the stain that you have been treating while it is still moist and let the powder dry overnight - or longer.
Magically, the stain is lifted by the powder - you can see the stain in the dry powder - and you vacuum it up.
If you can still see the stain, you can go to Clorox II - and that usually works.
White vinegar is another popular stain remover - but, I have had the best luck with milk and
Clorox II for the tough stains.
Part of the success depends on the carpet. All wool will soak up colors and want to hold onto them.
Synthetic fibers are easier to clean as they usually do not hold onto the colors in the same way.
There are tons of ink and stain removal tips online - and other products that you can try.
I get amazing results with Bestine, but it's a hazardous product.