Apple had no real case against Digital Research or anyone else over the GUI as Apple didn't invent it, as the courts ultimately agreed. That distinction went to Xerox who first showed their GUI to the world in the early 1970s, Apple were just one of the companies who copied it.
As part of their efforts to beat Microsoft, Apple legally attacked every GUI that ran on top of DOS, but without success. Interestingly, Apple ignored the non-DOS markets they didn't care about e.g. Commodore had a GUI called Magic Desk running on the C64 computer that pre-dated the Mac (IIRC). Magic Desk had a joystick controlled WIMP GUI, with file manager and document viewer, and would have also been the desktop GUI for the Commodore Plus/4 computer had the author John Feagans not left the company before finishing it. Feagans also later ported GEM for Atari without any legal challenges from Apple, nor did Apple go after Commodore (again) over the Amiga GUI.
While Digital Research agreed to settle with Apple it was not because they infringed on anything Apple made, it was purely to avoid an expensive court case that they couldn't afford. I sincerely doubt they would have agreed to make any changes to GEM at all if they had they financial resources to have been able to defend themselves from Apple's spurious legal claims. But even then, Digital Research only agreed to a few very minor cosmetic changes to GEM, concerning really crucial and innovative Apple inventions like err... changing a couple of icons and the appearance of the close window button, changing the width of the scroll bars, removing window open/close animations and shaded titlebars, and changing the default desktop view to the file manager! This changed version of GEM was released as GEM/2 and continued to be developed and sold by Digital Research without any further trouble from Apple.
Amusingly, one of the main developers of Digital Research's GEM was Lee Jay Lorenzen, who had previously worked at Xerox PARC in the 1970s developing their GUI. In effect, Apple took what was largely Lorenzen's work in the first place, implemented it on their own computer, then sued over his next GUI!
Apple also sued both Microsoft over Windows and HP over New Wave, alleging the theft of the 'look and feel' of the Mac GUI but as you may recall Apple lost both cases once it got to court. Apple later 'borrowed' much from both, ironically including the look and feel of HP's New Wave with it's 3D effect dot shading! Then, like now, Apple routinely use frivolous legal action to both try and harm their competition, as well as just another tool in their PR tool box which serves to perpetuate the idea that Apple invented something better or first. People mostly remember the initial headlines that scream alleged infringement on Apple's property rather than the end results which often don't emerge until years later e.g. whether Apple lost the case, settled, made a public apology, had their patents invalidated, etc. somehow never quite seems to get the same media coverage.