Parkinson's patients can do their best to ignore the stare
This should be your initial choice in the whole staring situation. And as always, it's easier said than done. But, ignoring the curious stare from the people around you won't only save your mood, but also helps you to avoid any trouble. If you show them that you are taking your tremor easily, then they might also stop caring about it, too. Sometimes, pretending that you don’t see them staring at you will make them drop it.