For this particular subject, I always turn to my personal source, Wire Faculty member Scrimshaw Mary of Nashville, TN. She responded with the following:
Oh my, a really good question for sure.
Ivory is a natural material and porous. It will absorb moisture out of the air and anything around it. Hence the reason to always store an ivory piece, (especially jewelry), in a plastic bag to give it a controlled environment away from the surrounding environment, such as low or high humidity. Is it stained and badly discolored or what? You cannot scrub any stain out, because once it is discolored, it is in there pretty much for good. What gives ivory that yellowing over time (that brings out the natural grain in the ivory) is human body oils from wearing and handling it.
A general cleaning can be done with a q-tip and baby oil to replace some of the moisture, and using a soft cloth to hand polish will help bring back some luster to it (but do not add polish). This can help remove any surface dirt from the beads. If the beads are carved, it will help to loosen anything in the cracks so that can be removed. Even working under a magnifying glass and using a needle or metal scribe can help loosen any caked in residue if done slowly and carefully so as not to scar the ivory itself and using the baby oil to soften up the foreign matter.
Never use water~! You cannot dip the beads in water or a solution of any kind and just leave them to soak. Being natural, the ivory will absorb the liquid and swell; once removed and dried, the moisture absorbed will slowly evaporate and the beads will crack, etc.
I have never done any real "restoration" work on old jewelry pieces. If there is another way, I haven't heard of it simply because, as you may know, I use the raw material to create my own shapes, cabs, etc. Unfortunately, I have no idea concerning nicotine and its effects on ivory or how long an "odor" to a sensitive non-smoker would be.
Answer contributed by Dale "Cougar" Armstrong