How does the gravitational influence of a single, distant star compare to the gravity from our own Sun on Earth?
It is utterly negligible compared to the gravity from our own Sun and the Earth itself
The gravitational effect exerted by any single star located across light-years of space upon Earth is overwhelmingly insignificant when weighed against the gravitational forces already acting upon us. The force we experience is dominated primarily by the mass of our own planet, Earth, and secondarily, but powerfully, by the mass of our immediate local star, the Sun. Even if the vector of a distant star's gravity were directed perfectly toward Earth, the sheer magnitude of distance ensures that this influence is entirely negligible in comparison to the local gravitational field that dictates planetary and orbital mechanics.

#Videos
Objects Fall from Space Where There Is No Gravity, Here's Why