HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\SyncMgr\Handlers
3 In there you should see a branch called: {08b0b2d5-3fb3-11d3-a4de-00c04f610189}
Right-click on the branch and select Delete from the context menu.
Restart your system and the icon should be gone.
{08b0b2d5-3fb3-11d3-a4de-00c04f610189} = SQL Server Handler
{750fdf10-2a26-11d1-a3ea-080036587f03} = Offline Files Handler
It seems you have your Offline Files feature still enabled. If not it is okay to remove its handler manually through registry using the method I described.
And don’t worry the worst case scnario would be that Sync Center would no longer work nor start on logon which is what you want, right?