There is nothing wrong in a woman working as telephone operator as long as she abides by the ethics and morals of Islam regarding talking between people of the opposite sex. While talking on telephone she has to avoid softening her voice and flirting in a manner meant to cause temptations.
As for those who regard woman’s voice as `Awrah, they have no authentic evidence supporting their opinion. Because in the lifetime of the Prophet (peace and blessings be upon him), women are allowed to voice their opinion publicly. The only prohibition is the female talking softly and flirting in a manner meant to excite and tempt the male. This is expressed in the Qur’an as complacent speech which Allah mentions insurat Al-Ahzab, verse 32,(‘O wives of the Prophet! You are not like any of the other women: If you do fear Allah, be not too complaisance of speech, lest one in whose heart is a disease should be moved with desire: but speak you a speech that is just.)
What is prohibited then is alluring speech which entices those whose diseased hearts may be moved with desire and that is not to say that all conversations with women is prohibited, for Allah completes the verse, (…but speak you a speech that is just.) (Al-Ahzab 33: 32).