If your baskets suffer smoke damage or if you purchase a basket that has been kept in a home with smoke, it may not be a total loss.  Here are a couple suggestions we can make:

... Older baskets with no color (prior to 1985) can be washed in mild soapy water, rinsed well and set to dry.  For newer baskets, you can try spraying it with a combination of vinegar/water and letting it sit in open air (outside if possible). If it has color, you need to be really careful with water because it can cause the colors to bleed.  

... For baskets later than 1985 or one with color, you can try placing the basket in a big plastic bag with a shallow dish of activated charcoal (can usually find in the aquarium section of a pet supply store).  Wrap it up tight in the plastic and let it sit for a few days.  We have also heard of people using vinegar, instead of the activated charcoal ... Sit basket in a closed bag with an open bowl of vinegar.