In grid instead of normal column use itemTemplate and place Textbox in it and then try to drag the div data to your grid. It won't reject your request :)
Try to implement following line of code in your GridView
<asp:GridView ID="GridView1" Runat="server" >
<Columns>
<asp:TemplateField HeaderText="AcceptInput">
<ItemTemplate>
<input type="Text" name="txtInput" runat="server">
</ItemTemplate>
</asp:TemplateField>
</Columns>
</asp:GridView>
I am sure this will work. If it doesn't please let me know.