I'd have to assume this is similar to cleaning wicker furniture. The individual wicker strands might be thinner and the weave different, but the idea is still the same as it's s till the same materials, whether it's real wicker or synthetic.
For routine cleaning of wicker that's made of bamboo, rattan, or willow, brush off or vacuum as much of the surface dirt as you can. Then wash it with a soft brush and soapy water to which you've added one or two teaspoons of ammonia. Rinse well and let the piece dry outdoors in the sun.
To remove grime from wicker furniture that's a more than just dusty, use a mild oil-base soap, such as Murphy Oil Soap, mixed with warm water. For a homemade cleaner, mix 1⁄4 cup ammonia, 2 tablespoons white vinegar, and 1 quart warm water. Follow any ventilation recommendations and other precautions outlined by the ammonia manufacturer on the bottle.
There are other sites that recommend similar ways to clean, some include equal parts of vinegar and water, so there's plenty of ways to make this work, and you evidently aren't going to hurt it with water. Remember that lots of patio furniture is made from wicker and is left outside in any weather purposefully.