How should one respond when a person of another faith greets with the Islamic greeting of peace?
With an equally warm or even better greeting. Whoever sincerely wishes you peace should be wished peace in return, whatever their religion.
Many Muslims live side by side with people of other religions. Sometimes a Hindu, Christian or other friend kindly says "Assalamu alaikum", which means "peace be with you". Some then wonder whether they may return this greeting in full.
The verse above gives the answer. Whoever is greeted should reply with a better greeting or at least return it. The verse makes no distinction according to the religion of the person who greets. A sincere wish for peace deserves a sincere wish for peace in return, such as "Wa alaikum assalam", "and peace be with you too".
The uncertainty comes from reports about one very particular situation. At that time some people deliberately twisted the greeting. Instead of "as-salamu alaikum", peace be upon you, they mumbled "as-samu alaikum", death be upon you. In this way the greeting became a hidden curse. To such words the Holy Prophet Muhammad (saw) replied only briefly with "and upon you". Even then he remained gentle, as the hadith above shows.
That situation must not be transferred to sincere greetings. Someone who deliberately turns a greeting into a curse is doing something entirely different from a friend who wishes you peace out of warmth. A sincere greeting is accepted gratefully and returned with the same warmth.
In this way the greeting of peace becomes what it is meant to be. It brings people together, even across the boundaries of religion.