Since the last couple of LO versions, pivot tables seem to be produced with obtrusive thick borders internally around the various elements. I’ve tried changing the pivot table formatting options (via F11), but I can’t get rid of them. Any ideas??
Try changing the option:
Menu/Tools/Options/LibreOffice/View- Use Anti-Aliasing
Thanks mariosv! Unchecking Anti-Aliasing did the trick. Not something I would have thought of 
What a relieve! Thank you for solution!