Microfiber cloth.
Casey

More wiping with a microfiber cloth, though if you used any solvent you may have made the problem worse.

I shop vac with a crevice tool might also pull it out.

Be very careful not to scratch with the crevice tool.

You may need to even sand the tool with 400 grit wet-or-dry paper to make it as smooth as possible.

A dry microfiber cloth isn't dong anything (and I don't have a shop vac.)

Brickeyee: you said the solvent may have made it worse. So I should stay away from the denatured alcohol? Would water be a better option?

Any other suggestions?

I'm wondering if I should rub over with another light coat of stain and quickly wipe it off. That would stain the dust caught in the grooves and the rest of the wood should be OK. I could then repoly and just seal in the stained-dust. Is that making a bad situation worse?

It doesn't look bad... but I don't want to make it worse! TIA!

You are supposed to use a cloth dampened with naptha if it is oil based and for waterborne use water plus 5% denatured alcohol. I have used water based analine dye in the way you asked about, Seemed to work ok. In any case, use a colored wax, like Minwax Furniture Wax Dark. Don't use Bree Wax for this because it will mar the finish.

Any solvent can cause the dust to cake together more tightly and be that much harder to remove.

Even if the solvent cannot actually dissolve the material, just like adding liquid to powder in baking you can create 'lumps' that are hard to break up.

If there is a lot of buildup you might try a very soft tooth brush. and even some dry baking soda with the tooth brush.

At this point, wipe on a small amount of the finish with a cloth and see if the dust disappears. You may even prefer the wiped-on finish.
If the pores are still ishy, wipe off immediately with thinner.
Casey

Thanks all for your advice. I went over it again with the microfiber, and then wiped a thin coat of stain into the grain with a rag. I wiped off all excess stain immediately and let it dry. Thin coat of poly and I'm done! It looks great! Thanks for your help!