Upstream is the solar apex, the place in the sky the sun seems to be rushing towards, due to our place in the galactic rotation. Its in the general direction of the star Vega. Except Vega wasn't there when the object was cruising through its present vicinity. Vega also has its own proper motion through the LSR. In the time it takes this object to travel even one light year, the night sky changes completely in appearance as the stars slowly wander around the Local Standard of Rest, moving at speeds roughly comparable to the object. And Vega is a relative neighbor, only 26 light years away.

After it's slingshot around the sun, I don't know where this rock is headed now, but at its current speed it won't be getting anywhere for thousands of years. You have to keep in mind, any technology capable of interstellar travel speeds will not have to rely on gravity-assist maneuvers.

If this object was ejected from some other solar system, it may have happened many billions of years ago; both the sun and its parent star may have made many revolutions about the galactic nucleus since then. Its parent star may not even exist any more. This is just another mote of dust adrift in the void. Just like us.