Ah, I misread that completely. You said the links folder itself, not some other random link. Sorry.
Here ya go:
Try this one first and if that doesn't work for you (may not be correct for your version of IE), then try the below steps:
http://support.microsoft.com/kb/179599
Other method:
This involves editing your registry, back it up first. If you don't understand what you are seeing in the registry and the instructions below, don't do it.
Here are the steps:
Click on Start Button > Run > Type: "regedit"
Go to this key: HKEY_CURRENT_USER\Software\Microsoft\Internet Explorer\Toolbar
Once there, check out a stringvalue called "LinksFolderName". Simply doubleclick it and delete the value data.
Next, go over to this key: HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Policies\Explorer
Once there, rightclick and create a DWORD Value and name it "NoSaveSettings".
Let me know if you have any more questions.
http://www.google.com/search?hl=en&q=favorites+links+folder+delete