That's not really possible, by the means with which you are attempting to do it. Response.Write is processed on the server and so are the ASP.NET controls, there's no way to register text written to the page as a control by Response.Write.
There are other options you can use for ASP.NET, such as the PlaceHolder control. If it is something that you need to show for some users and hide for others, you can use the Visible property of the textbox control, eg:
Code:
<asp:TextBox id="TextBox1" runat="server" Visible="False" />
Regards,
Ax