Getting Cigarette Smell out of a Basket

I use fresh dry coffee grounds. Place them in the filter & set it down in the basket for a few days. This works well for musty smells, etc.

White vinegar rubbed on generously should get the smell out. Good luck

Sprinkle it with Baking Soda and close it up in a brown paper bag for a day or so, this works for books, so i think it will work for your basket too

Baskets are made with fibers wet, so any wet solution won't harm it. I would try leaving it outdoors in sun and wind for a few days. a baking soda solution would be cheap to sprinkle on, spray with water, let dry...

Wrap charchol in newspaper and put in basket. Put basket in plastic trash bag along with lots of crumpled up newspaper. Close bag. Check it in a few days. I had one I had to leave in almost a month.

How about some Febreeze? That wouldn't ruin the basket. Good luck!!