KIll the browser window after it launches another browser window in IE using the following vbscript:

Set oShell = CreateObject("WScript.Shell")
If oShell.AppActivate("type the IE window title you want to close here") Then
WScript.Sleep 500
oShell.SendKeys "%{F4}"
End If
 

Just place the path of the vbscript in the OSD file in the following XML tag:

<DEPENDENCY>
<SCRIPT EVENT="LAUNCH" TIMING="POST" PROTECT="TRUE" WAIT="TRUE">
<SCRIPTBODY>type the name or path to the script here eg. killtask.vbs</SCRIPTBODY>
</SCRIPT>
</DEPENDENCY>

After you launch the appv package, the vbs script will kick in and kill the browser window you defined in the vbscript.

Job done :)