For anyone wondering about the title, by "trap" they mean "detect destructively": there are no stable neutrinos in a bottle in this article.
Whatever gravity “trap” you make is going to pale in comparison to the gravity wells around us (earth, the sun, etc) and the weak force scales exponentially with energy. So a slow-moving neutrino would interact even less with the weak force than a relativistic one.
But they interact with things even less than relativistic neutrinos. Even a light-year of lead wouldn’t be enough to register a hit from one.
They’d be all around you, but you would have exponentially smaller chances of interacting with them.