Figure Analysis
These guys are eunuchs too, but unlike Hegai and Hathach who are positive characters, they're plotting to assassinate the king (though, this might not be a bad idea, given some of Ahasuerus' behavior like approving massacres and stuff). They're disgruntled employees. Fortunately, Mordecai overhears them conspiring and he reports it to Esther… who reports it to the king, who has them executed, and which proves to be helpful to Mordecai later on when the king remembers his service.
Ultimately, what turns out to be lemons for Bigthan and Teresh ends up being lemonade for Mordecai and Esther.