Apple's iPhone Software, is indeed one of the most advanced mobile operating systems ever made. Being introduced a few years ago, we have seen its neat evolution every year. Nevertheless, there might be system bugs that could cause you a headache, from simple stuff to real functional stuff.
A system restore is always a good solution when it comes to bugging issues in any software. Apple designed all devices with a customizable profile you can back up, and store in your PC. This is very functional when upgrading your iPhone, cause all your contacts, music, mail, calendars, and home screen layout will be stored in the back up. Regrettably, small bugs are also stored within the back up.
I performed a deep research finding several suggestions on this problem, some real stupid things, and some reasonable. People would suggest a restore, but that won't take that bug out of your device's profile. They also suggest a restore without using your back up profile, but that's not a viable solution for those of you who already have a whole network, ringtones, music, contacts, mail, calendars, and other sort of stuff that would take a lot to re-configure on a new profile.
The first thing you'll need, is to access the system raw files. You can do this by either using a Mobile Finder, using a FTP/SSH method using a software (Google it if you're not familiar with the term), or use a direct files' browsing tool for iPhone, iPod, and iPad.
I personally use i-FunBox software whenever I need to browse my device. I find this as the most useful tool for these kind of tasks. Regrettably, there is no Mac version available yet. You may download the software here.
Go ahead and delete the icon from your home screen by pressing and holding the icon until it jiggles. Then press the delete "X" on the corner. The system will store an "invisible icon", or also known as "invisible bookmark". Once you're in your system files, go to the following folder:
private/var/mobile/Library/WebClips
Delete everything inside the WebClips folder. Then reboot the device, and voilá. Your customized home screen bookmark will be there no more. If you experienced this issue, you may well know that rebooting, or syncing would bring the icon back up.
If you have any feedback, or any further findings, let us know or follow my Twitter @ViNnyb0ii