HELP! cannot remove blank icons from home screen

I have an iphone 4 that used to be jailbroken and now it's not. I am desperately trying to find a way to remove these annoying blank icons. I can press down on the screen until the icons wiggle and delete them, but later when I update or back up my phone the icons appear again! How do I permanently delete them WITHOUT re-jailbreaking my phone? Is there a way to ssh without jailbreaking? I don't know a ton about computers so any help is appreciated!!