The short answer: vacuum it with a brush attachment, wipe it with a barely damp cloth, and dry it in shade rather than sun. Do not submerge it, and the reason is not the fibre. Almost every seagrass and water hyacinth storage basket sold is woven onto an iron or metal wire frame, which the manufacturers state plainly on their own listings. Soak one and the wire rusts inside the weave where you cannot see it, then bleeds through and stains the basket from the inside out months later. And if the basket smells, take the liner out and wash that: most come with a removable cloth lining, and it is usually the liner rather than the basket that has absorbed whatever the smell is.
Disclosure: this post contains affiliate links, and as an Amazon Associate I earn from qualifying purchases. If you buy through them I may earn a small commission at no extra cost to you. I only recommend things I would use in my own home.