Apparently this is the tradition in Nepal and India. I have no idea why people feel the need to do this. The practice is popular enough that there is even a clothing store called "New Pinch." My only theory about the origins of this practice is that St. Patrick's Day is not really celebrated in Nepal and there was a maw in the deep socio-psychological milieu that could apparently only be filled by pinching strangers.
So I looked to the Internet to provide further illumination, as is my wont. This is from a Q&A website like Yahoo Questions (here):
"Q: What is idea behind doing NEW PINCH when someone wears new dress ?
Best Answer: Usually the person's mentality changes for a moment and will be in a flying mood
NEW PINCH is to indicate him/her that come-out of dream (that you are predominant) thereby bringing him/her to real world, at the same time an appreciation and admiration about the selection and how it suits the person well, will increase cardinal relationship"
Mystery solved! Thanks, the Internet!