Why does Kepler's "Big Picture" of comet 67P look so strange? And what is the significance? The observation of comet 67P by the Kepler space telescope has been reported in various science news outlets recently. For example, the image below appeared in the recent NASA news article NASA's Kepler Gets the 'Big Picture' of Comet 67P and the same or similar images can be seen elsewhere. The article says:

From Sept. 7 through Sept. 20, the Kepler spacecraft, operating in its K2 mission, fixed its gaze on comet 67P. From the distant vantage point of Kepler, the spacecraft could observe the comet's core and tail. The long-range global view of Kepler complements the close-in view of the Rosetta spacecraft, providing context for the high-resolution investigation Rosetta performed as it descended closer and closer to the comet.
During the two-week period of study, Kepler took a picture of the comet every 30 minutes. The animation shows a period of 29.5 hours of observation from Sept. 17 through Sept. 18. The comet is seen passing through Kepler's field of view from top right to bottom left, as outlined by the diagonal strip. The white dots represent stars and other regions in space studied during K2's tenth observing campaign.

I don't really understand this image. It is a GIF assembled from several exposures, but in each frame, individual stars appear as tight clusters of dots for some reason, and the comet moves within a bright, narrow band that crosses the entire image in all frames. Why does this looks so strange?
Also, what is the importance of Kepler deviating from it's observations to concentrate on 67P during this period? What is the scientific importance of this series of observations?

above: Image credit: The Open University/C. Snodgrass and SETI Institute/E. Ryan From here.
One thing to keep in mind is that the Kepler instrument is not a telescope like Hubble.  It is a photometer and though it uses CCDs to look at the sky, it doesn't return a picture in the usual sense.  The way it operates is that you only look at the pixels around the object you're interested in because otherwise you'd never get all those pixels transmitted to the ground because there are so many of them.
To observe the comet, they looked at the track it would make across the Kepler field of view.  They chose only the pixels you'd need to look at the comet and its tail, and this turned out to be a 15-pixel-wide swath across the detector.  That band across the image you see is that swath.  You'll notice that most of the picture is black, which are all the pixels that they didn't look at.
The stars in the scene where the image isn't back are the stars that Kepler was also looking at.  However, I'm not intimately familiar with raw Kepler data so I can't tell you why the stars are in clusters of four.  Because all the stars are lined up in the same direction, I would surmise that this is because Kepler was tracking the comet and the stars were moving in the background.  From the way they were going to take the measurements, each 36 hour observation was made up of three observations, so I am at a loss as to why there are four dots per star when this would suggest there would be three.
The answer to the science question can be found from the observation proposal.  To summarize:

Kepler photometry can provide the following key measurements at a time
when no other platform can observe the comet:

Total brightness of the comet. This relates directly to the amount of dust being released and therefore gives a critical ‘total’ activity
measurement, which can be compared with the instantaneous (but local)
measurements from various instruments on Rosetta.
Variability of the comet. There are two sources of variability; changing amounts of dust in the coma, and the underlying light-curve
of the nucleus (its non-spherical shape reflects more or less sunlight
as it rotates).

The measurements from Kepler will extend the total activity curve to
almost the end of the Rosetta mission, meaning that data in the last
months of Rosetta will not rely on extrapolation of the earlier
Earth-based observations. As the final months will be some of the most
exciting – as Rosetta spirals down and makes local measurements from
incredibly close to the nucleus – this context information is very
important in this phase.