Final working code.

One draw back of this code, if you receive a valid email followed by an
invalid email, this will cause the Icon to be removed.

In the Add-In Class

//MailManager object in the Add-In
private MailManager _manager= new MailManager();

//applicationObject is Microsoft.Office.Interop.Outlook.Application
applicationObject.NewMail += new
Microsoft.Office.Interop.Outlook.ApplicationEvents_10_NewMailEventHandler(ap
plicationObject_NewMail);

//Event Handler for Microsoft.Office.Interop.Outlook.Application.NewMail
event
private void applicationObject_NewMail()
{
_manager.CleanInbox(this.applicationObject);
if(_manager.RemoveIcon)
 _manager.RemoveNewMailIcon();
}

//Class to encapsulate Inbox Cleaning
public class MailManager
{
//Function pointer to Callback
private delegate bool EnumWindowProc( IntPtr hwnd, int i);
private bool _removeIcon = false;

[StructLayout(LayoutKind.Sequential)]
internal struct NOTIFYICONDATA
{
 public int cbSize;
 public IntPtr hwnd;
 public int uID;
 public int uFlags;
 public int uCallbackMessage;
 public int hIcon;
 public string szTip;
}

[DllImport("user32.dll")]
 private static extern int SendMessage( IntPtr hwnd, int msg, int wParam,
int lParam);

[DllImport("user32.dll")]
 private static extern int GetClassName(IntPtr hwnd, [In][Out]StringBuilder
lpClassName, int nMaxCount);

[DllImport("user32.dll")]
 private static extern int EnumWindows(EnumWindowProc callback,int lParam);

[DllImport("shell32.dll")]
 private static extern int Shell_NotifyIcon(int dwMessage, ref
NOTIFYICONDATA lpData);

public MailManager()
{
}
//Property if the mail should clear the Icon
public bool RemoveIcon
{
 get{ return _removeIcon;}
 set{_removeIcon=value;}
}

public void ValidateNewMail(object item)
{
 //Here is where I deteremine whether to keep to toss item.

 Outlook.MailItem mail = item as Outlook.MailItem;
 _removeIcon=false;
 if( mail != null)
 {
  if( mail.Subject == "InterScan NT Alert")
  {
   mail.UnRead = false;
   mail.Delete();
   _removeIcon=true;
  }
  else if( mail.Attachments.Count > 0)
  {
   Outlook.Attachment attachment = mail.Attachments[1] as
Outlook.Attachment;
   if( attachment != null)
   {
    if( attachment.FileName == "InterScan_SafeStamp.txt")
    {
     mail.UnRead = false;
     mail.Delete();
     _removeIcon=true;
    }
   }
  }
 }
}

//Loops through all items in the Inbox.  New Items are Validated.
public void CleanInbox(Outlook.Application outlook)
{
 Outlook.NameSpace ns = outlook.GetNamespace("MAPI");
 Outlook.MAPIFolder inbox =
ns.GetDefaultFolder(Outlook.OlDefaultFolders.olFolderInbox);
 int i= inbox.Items.Count;
 while( i > 0 )
 {
  try
  {
   Outlook.MailItem mail = inbox.Items[i] as Outlook.MailItem;
   if( mail.UnRead)
                         ValidateNewMail(mail);
  }
  catch{}
  finally
  {
   i--;
  }
 }
}

public void RemoveNewMailIcon()
{
 EnumWindows( new EnumWindowProc(this.EnumWindowCallback), 0);
}

private bool EnumWindowCallback(IntPtr hwnd, int i)
{
 bool bReturn = true;
 StringBuilder sb = new StringBuilder(64);
 GetClassName(hwnd,sb,64);
 string sClass = sb.ToString();

 if( sClass =="rctrl_renwnd32")
 {
  if(KillNewMailIcon(hwnd))
  {
   bReturn = false;
   SendMessage(hwnd,1031,0,0);
  }
 }
 return bReturn;
}

private bool KillNewMailIcon(IntPtr hwnd)
{
 bool bReturn= false;

 NOTIFYICONDATA nid = new NOTIFYICONDATA();
 nid.cbSize =Marshal.SizeOf(typeof(NOTIFYICONDATA));
 nid.hwnd = hwnd;
 nid.uID = 0;

 int hResult;
 hResult = Shell_NotifyIcon(2,ref nid);
 if( hResult != 0)
  bReturn = true;
 return bReturn;
}
}