Good answers all but I would just like to add that the grit is always at the bottom of the holding vessel and as you pour it usuallty is with the small last percentage of liquid. This is where you can choose to stop pouring or very carefull strain.

Paper coffee filters, lining a strainer with cheese cloth, or a clean tea towel (NOT terry cloth) or one of those gold mesh coffee filters all work well. Lift out the rehydrated mushrooms with a slotted spoon (gently, so the grit settles), then strain the soaking liquid into a measuring cup or dish, and discard the grit, or rinse it down the drain. Then use your straining liquid in your dish, or as a stock. Especially good in risotto !

I've got a rigid plastic, re-usable coffee filter in the kitchen I use for this. dishwasher safe and inexpensive.

Then once you strain that soaking liquid, make it into a nice finishing sauce for your stir-fry: stir in some cornstarch, soy sauce, chili paste, miso paste, brown sugar and any aromatics you like. Pour this into your pan when your food is almost done and keep cooking and stirring until it's thick and coats the food!

Agreed--I've found that I need the fineness of a coffee filter to remove all the grit--I've even noticed it after straining through a jelly bag. I usually use a paper one--the gold filter I keep in my machine is fine enough but I'm usually too lazy to clean it for non-coffee purposes.

Use a very fine mesh strainer or a coffee filter or a triple layer of cheesecloth.