In the databind event handler of your datagrid check for the dateoccured on
each row and hide the button(s).

<asp:GridView ID="MyGrid" runat="server"
OnRowDataBound="MyGrid_RowDataBound" ........ />

protected void MyGrid_RowDataBound(object sender, GridViewRowEventArgs e)
{
   if (e.Row.RowType == DataControlRowType.DataRow)
   {
       if (Convert.ToDateTime(e.Row.Cells[0].Text) <
DateTime.Now.AddDays(-7))
       {
           e.Row.Cells[2].FindControl("MyEditButton").Visible = false;
           e.Row.Cells[2].FindControl("MyDeleteButton").Visible = false;
       }
   }
}

Obviously, change the column indexes as necessary.

N.B. setting a column's control(s) Visible property to false isn't the same
as hiding the column, which was the title of your OP...