Hill sphere
The volume of space within which an object can be said to orbit Jupiter is defined by Jupiter's Hill sphere (also called the Roche sphere). When the comet passed Jupiter in the late 1960s or early 1970s, it happened to be near its aphelion, and found itself slightly within Jupiter's Hill sphere. Jupiter's gravity nudged the comet towards it. Because the comet's motion with respect to Jupiter was very small, it fell almost straight toward Jupiter, which is why it ended up on a Jove-centric orbit of very high eccentricity—that is to say, the ellipse was nearly flattened out.