You can only reduce it's effect. If you become too aggressive in trying to reduce noise, you will change the acoustic characteristics of the word you're actually trying to clarify...meaning, you could easily change the vowel/consonant sounds of a word when eliminating noise.
Nonsense! I do digital data processing of seismic data for a living. We remove noise all the time with band-pass filters. The cell phone noize would have a certain frequency range and can be easily removed.