PowderChalk on Deep-pile Tight Carpet

Fine powdered construction chalk used on cord to make lines on flat surfaces (for cutting, truing, what have you) inadvertently got on my 4 year old deep-piled carpet. It's water-soluble... so it appears. However, in discovering what it is, I used water and now it's deeper down the pile.
They started as two dark specs. Then I took a wet rag to one and it turned bright reg. That's when I realized what it was. Must have been on a cuff of my work pants as I passed in my stocking feet.
Any idea of how to get this put? I used a Green Machine but stopped short thinking I'd just make a liquid that would go all the way to the mat. Aside from a wet towel and careful rubbing (synthetic fiber tufts) I really don't know what else to do.
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I would use a carpet machine so I could suck up the water as it sprayed into the pile.

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