I'm not sure if there is a way to prevent that folder from coming back, but I have a solution that works for me:
1.) From the Internet Explorer Favorites menu, right-click on the "Links" folder and choose Properties.
2.) Click the Hidden attribute at the bottom of the Properties page, then click OK.
3.) Restart Internet Explorer.
The folder will still exist within your file-system, but it will no longer appear in your Favorites menu.
I hope that helps!