Once in TNagar bus stand a senior person starred me on the road, I also noticed his starring. After a minute both of us recognised. He was big uncle to my sister in law who was in Jamshedpur and we met three years back, at the marriage of my brother. It was really happy to me on his remembering me.
Second time in the city bus when I was moving to office, a man of age similar to me starred at me by standing three persons ahead. Slowly he approached me and asked by saying my name. On my affirming with confusion he told that he was devarajan my classmate during schooling at Madurai. It took more than 10 years.
Smiling at them is fine as at times we will have to smile at strangers. Also greeting that stranger will help them understand that you noticed them staring at you. We are not losing anything by lending a smile of ours or by greeting them. So be cool and let go.
I have experienced similar situations in shopping malls or parks, I just smile at them. That's all.
"Do not give up, things might not favour you always"
In our country, sometimes such staring is an unconscious signal to become familiar and enter into conversation during long journeys. In such cases the person stared at responds by a smile and the starer then starts courtesy questions like where are you going or where from you have come etc.
It also comes as a natural alertness as a safety precaution measure. When we are new to a place, the locals immediately recognise that we do not belong to that place and then they stare at us to gauge and guess who we may be.
Do what inspires you !!