Fix drywall around electrical box
I would demo the entire back splash area removing all the Sheetrock.
Trying to save 10$ (about a sheet) makes no sense to me because the Sheetrock gets damaged or has residue on it. I would rip&amp; strip the tile and Sheetrock out and then if replacing with Sheetrock use green board or if tile use backer board to replace the Sheetrock.
Replacing a large piece will look better in the long run and save a lot of time. For the cost of 1 maybe 2 sheets.
If you cut just above the tile this can help keep the strip narrow but I usually go close to the cabinets as seams up there are the easiest to hide as they are not in direct view.