Look for the following element in the MasterPage code: 

<SharePoint:UIVersionedContent UIVersion="4" runat="server" id="PlaceHolderQuickLaunchBottomV4">
<ContentTemplate>
<ul class="s4-specialNavLinkList">

Above the bold section, add the following line of code: 

<Sharepoint:SPSecurityTrimmedControl runat="server" PermissionsString="ManagePermissions">

Change the blue PermissionsString value to whatever you want. Multiple permissions can be separated with a comma (no spaces). Note it should be a permission your target user(s) do not have, and has to come from this list. Spelling and case-sensitivity is important. Finally, add the closing tag after the SharePoint:UIVersionedContent closing tag: 

</SharePoint:UIVersionedContent>
</Sharepoint:SPSecurityTrimmedControl>

Original:
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