Compact Framework, which the .net runtime running on Windows Mobile, does not support button or other elements within a datagrid. Only EditBox is supported by default.
There are already questions and answers on how to add a button or checkBox to a compact framework datagrid here at stackoverflow:
How to add a button to a compact framework DataGrid?
Attach button to column datagrid in C# Compact Framework .Net 2.0
and
display images in datagrid with Compact Framework
and at other sides like: http://social.msdn.microsoft.com/Forums/en-US/caee833d-f0ac-496f-b13c-b87116450f39/how-to-add-a-button-in-a-datagrid
The solution is to add a custom paint handler for datacells.
There are also commercial extended datagrid controls available that support more than only EditBox: for example Resco SmartDrid control: article at codeproject. I am sure there are other vendors too. Just use a internet search "compact framework datagrid add button".