Fine Powdered Chalk on Deep Pile Thick Carpet

It seems you started with the wrong trick. I suggest waiting for it to totally dry and then use a vacuum with a beater bar and see if that does not work. It's going to be tough now that you got it deep in the carpet.

However ... I have not tried this under the conditions you noted. Wait a while before you try it and see if someone else has some advice they have tried.

If it's chalk (Calcium Carbonate) is not soluble in water, but is soluble in carbonated water. Whatever coloring was used is another matter. If, for example, an organic dye was use, strong acids may dissolve it (i.e., fuming Nitric Acid - wear a Kerry-suit).

Calcium Carbonate does react with weak acids (i.e., vinegar) to produce elemental Calcium and gunk.

I assume you have some of the original chalk. Experiment.

FYI, most nylon carpet is dyed in an acid solution. Because of this, I wouldn't use any acid in the presence of a dye. You're likely to A) strip some of the existing dye. or B) Cause the new dye (i.e. from the chalk) to attach to the fiber.

The acid thing is why kool-aid stains are tough to get out of carpet. In the carpet manufacturing business, the industry standard for stain resistance used to be to heat cherry Kool-Aid to some ridculous temperature and immerse a swatch of carpet, followed by immediate rinsing in cool water. An excellent way to turn beige carpet pink!

At this point I suggest you call in a good pro to first remove the stains, then clean the entire carpet to match the clean spot.

Not bad advice.

BTW I did find out something interesting while in one of their offices one day. Their primary cleaner/stain remover was Ivory Snow. Yep, the stuff from the grocery store. Some may use other products, but this company did not send their trucks out with anything else. They found they had a lot less problems with damaged carpet and it worked.

Woolite makes a new carpet spot cleaner in a blue bottle that is worth a shot. TOp rated by Consumer Reports and gets out all kinds of old stains in my 8 year old carpet that other spotters did not handle.