Citrix Published App - Close/Minimize IE Window

Let me try to explain my issue:
I have an application from a vendor that launches via ASP.  There is a client installed on my Citrix Server and the client simply launches a browser connection to the IIS server and then a Login dialog box is received outside of the IE window.  The problem is this.

The IE window never closes.  The application launches outside of IE and all work is performed in that window.  I dont want a browser window running from my Citrix server just sitting on the users desktop.  The vendor has no solution for this, but I would like to at least have the browser window minimized and out of the way.  Any suggestions on how I might accomplish that are appreciated.

Thanks in advance,
ChrisStart Free Trial