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I wouldn't be too quick to thank ol' Jinkers.
There's probably as much chance of Jupiter's gravity throwing an object *onto* a collision course with earth, as there is of it throwing something *off* such a course. Admittedly, anything that gets too close to Jupiter probably gets swallowed up completely.
Even worse would be if Jupiter fragmented a large single body into lots of smaller (but still significant) bodies. One of the pieces might do a bit less damage during an earth impact than the whole would have, but having more of them out there might increase the chance of an impact occuring at all. Old man Jupiter might be a mixed blessing.