Hi Anteshwar,
If you want to remove Exchange 2003 from your coexistence environment, please perform the following procedure:
1. Move all mailboxes to an Exchange 2010 server in the organization.
2. Move all content from the public folder database on the legacy Exchange 2003 server to a public folder database on an Exchange 2010 server in the organization.
3. On Exchange 2003 servers, for each offline address book (OAB), move the generation process to an Exchange 2010 server.
4. Verify that Internet mail flow is configured to route through your Exchange 2010 transport servers.
5. Verify that all inbound protocol services (Microsoft Exchange ActiveSync, Microsoft Office Outlook Web App, Outlook Anywhere, POP3, IMAP4, Autodiscover service, and any other Exchange Web service) are configured for Exchange 2010.
If all above steps have been prepared, we can remove the last Exchange 2003 server from the Exchange 2010 organization from ADSIEdit. For detailed steps about this, please refer to:
https://technet.microsoft.com/en-us/library/gg576862(v=exchg.141).aspx
Regards,