Let me see if I can explain the main aim and accomplishment of this work.
First off: the picture you're puzzling over is a "luminance RGB" image, in which the bright regions are represented by color (a sort of pseudo-true color using near-infrared images), with the second faintest parts represented with black and the very faintest parts with white. The latter aren't qite "garbage", as Hobbes suggests in their answer, but they are relatively speaking the noisiest parts of the image, so there's little real information be found there.
This paper (Borlaff et al.; see the link in Hobbes's answer) is about re-processing near-infrared HST images originally taken about ten years ago as part of the Ultra Deep Field. Previous processing of these images (e.g., Koekemoer et al. 2013 ["HUDF12"] and Illingworth et al. 2013 ["XDF"]) was focused on getting information about the smallest, faintest galaxies, which are mostly the really distant, high-redshift galaxies. Because of this, the crucial stage of sky subtraction had some biases: in particular, it tended to treat the faint outer regions of the large, nearer galaxies as part of the sky to be subtracted. This is actually fine for the analysis of the small, distant galaxies, but means that if you do want to analyze the outer regions (outer disks, faint stellar halos, remnants of merger structures, etc.) of the larger, closer galaxies, you have the problem that their outer regions are over-subtracted (hence the "missing light") and thus unmeasurable.
(The "sky" being subtracted is a combination of emission from certain atoms in the tenuous outer atmosphere above HST, sunlight scattered from dust grains in the inner solar system, and the so-called "extragalactic background" = the combined light from unresolved distant galaxies.)
The abstract mentions four improvements the new study implemented when they re-processed the HST images: "1) creation of new absolute sky flat fields, 2) extended persistence models, 3) dedicated sky background subtraction and 4) robust co-adding."
I would suggest that the third item is perhaps the most important: they implement a method which does not subtract off the faint outer regions of the larger galaxies, and thus the resulting images still have information about the outer parts of these galaxies.
The plot below (extracted from Figure 20 of the paper) illustrates the kind of improvement they were after. It shows the surface brightness (in the F105W near-infrared filter) of one of the largest galaxies (a giant elliptical -- I think it's the big, round, yellow galaxy in the lower middle of the color image) as a function of radius (measured in elliptical annuli). The red triangles were measured using the XDF-processed image, the blue squares used the HUDF12-processed image, and the black points use the newly re-processed image produced as part of this paper [ABYSS]. You can see that the XDF points drop off at a radius of about 55 kpc, the HUDF12 points fall off at around 90 kpc -- but the light from this galaxy can be traced out to 140 kpc in the ABYSS-reprocessed image. This also means you can potentially analyze structure in the outer part of the galaxy out to ~ 150 kpc, which wouldn't be possible with the previous versions of the image.
(I should point out that I'm friends with, and have co-authored papers with, a couple of the authors, so I may be a bit biased -- but I think this is really impressive work!)