I don't think that this shift has anything to do with cross-link density. This rather seems to be a measurement of the nanoparticles' diffraction pattern. You can determine the degreee of crystallinity with SAXS, but not the cross-linking density and not with XRD. I wouldn't necessarily believe the interpretation of the authors.
I think the difference in XRD shift is because of a change in crystallinity. Then, they hypothesized that this change is because of crosslinking between nanoparticles and hydrogel chains. Am I right?
I don't know what kind of gel that is, but usual semicrystalline polymers have crystals that are simply too large to be measured with XRD. XRD can measure only spaces up to 8 nm. You need a SAXS to measure larger distances. They hypothesize indeed that there the change is due to a cross-linking reaction, but this is clearly overinterpretation.