I am American, my husband is American, and until the media coverage of the recent horrific rape in India, we had never heard of the term "eve-teasing'. We are mystified as to how this term of obviously Western and Judeo-Christian origin entered Indian English. The OED offers no history, other than citations dated from about 1960, about this term. How did this term enter Indian English? Is 'eve- teasing' a British concept? Or did Indians learn the words "eve" and "teasing" separately, and apply the term to public sexual harrassment (and worse) of a female?
The symbolism, if drawn from English scripture and nothing else, would appear weak and muddled if not outright nonsensical, especially considering what all available from the vast stores of myths and histories of cultures the world over.
One other possible root, more plausible, and making the two even more so together, must be the myth some Eastern men entertain, that of the European woman as an exotic sexual symbol.
If true, such connection explains why the phrase was not part of British English. And also why, one might predict, its use will not spread geographically beyond its current domains, except when to reference directly that event, which within not a month's time had simultaneously narrowed and condensed its meaning and propelled it to world consciousness.
Having not heard this term until the first post, I asked an Indian colleague about it. He would not apply the term to the "worse" mentioned by thorhild. He likened it more to the catcall behavior practiced by construction workers before the term sexual harrassment became widespread; it always stopped short of physical contact.
He believes the 'eve' part did come from the Adam and Eve of the Bible. (Note: India has been innundated with missionaries since about 1600. Tradition has it that Thomas (one of Jesus' 12 disciples) started some churches in India in the first century. Eve as the mother of all living and as the prototype of all women is a concept which would probably have a long history in India.)
I collected a number of citations for this term a few years ago and wrote up an entry for it. Don't forget to search this site when thinking about language!