The major component of tahini is sesame. Sesame seeds fall under the general class of kitniyot, foods that Ashkenazim (and some Sephardim) may not eat on Passover.
This was enacted because kitniyot are similar in texture to chametz, so the uneducated observer may mistakenly conclude that chametz can be eaten on Passover too. This prohibition includes also beans, rice and corn. This injunction was unanimously accepted by Ashkenazic Jews; many Sephardic Jews, however, continue to eat kitniyot on Passover. If you are Sephardic, speak to your rabbi to determine your family and community tradition. Obviously, even for Sephardim, tahini would need to be certified kosher for Passover to insure that it is chametz free.
The prohibition is only with regards to consumption of kitniyot; there is no obligation, however, to destroy or sell kitniyot products before Passover.
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