The Torah, in our sedra, prohibits tattooing: "You shall not make gashes in your flesh for a dead person; you shall not etch a tattoo (ketovet ka’aka) on yourselves. I am God." (this is the only time this word appears in Tanach)." The issur - either because it is associated with idolatry, or because it is an unnecessary cutting into the skin - only applies if the skin is perforated and the resulting hole filled with ink. A Jew with a tattoo may certainly be buried in a Jewish cemetery, despite popular misconceptions (including those made in episodes of both Curb and The Nanny). There is no obligation to remove a tattoo, a process that can be painful & expensive (though those with obscene or non-Jewish symbols may indeed opt to do so). A woman once asked Rav Ephraim Oshry, the well-known posek who wrote responsa during the Holocaust, if she could remove her concentration camp tattoo via plastic surgery. He advised Holocaust survivors not to remove their tattoos, but rather to wear them as badges of honor. But this would not apply to later generations who want a similar tattoo matching those of the survivors.
Beit Midrash Torah Portion and Tanach Kdoshim