Ms. Teschmacher is a personal assistant to James Olsen, and previously a personal assistent to Cat Grant. She had a thing for Mike Matthews (Mon-El) and was caught having a "fling" with him in a copy room by Kara Danvers.
Eve was eventually revealed as secretly being in Lex Luthor's employ. He used her to infiltrate his sister Lena's organization and get close to her.