The other thing (or thing and a half) would not really violate the inverse square law, but only seem to violate it. That thing would be an attractive (or repulsive, hence the "and a half" literary vehicle :)) force with a source located so far away as to make the force gradient so gradual as to be below any threshold of measurement. (At close range, the gradient is very steep, at long range, it becomes increasingly consistent.)
So, perhaps there's a large, (perhaps dark) object located somewhere far to the other side of the Sun from the probe, exerting a slight pull, apparently constant due to the great distance from the probe.
However, if the effect is seen on two probes that are aimed in different directions relative to the Sun, then it would shoot that theory down.
Maybe it's just the aether wind, flowing towards the Sun. :)
I disagree. Freepers will arrive at possibilities nobody else will think up. Maybe not realistic possibilities. Maybe somebody up there doesn't want us traveling to other solar systems.
You would be surprised what scientists don't think of. :)