Is there a way to restart all the scripts on the page?

My problem is as follows.

I have a div#resultado , which contains a table which is filled with data that I consume from a WebService. In this table there is a button for each row that activates a modal to modify the values of the row.

<button type="button" class="btn" name="btn_Mcontactos" id="btn_Mcontactos" value="{{contactoId}}">
    <img src="public/img/carpeta.png" alt="Ver" style="height:25px; width:25px;" />
</button>

When I insert a new value in the table, what I do is that I update the content of div#resultado (I create the table again via AJAX). The problem is that when I click on the button of the table nothing happens, I imagine that the script that shows the modal is not activated.

Is there a way to restart the scripts without reloading the page?

Code: show and fill modal of the contact to edit

  $("button[name='btn_Mcontactos']").click(function(){
         var valor = $(this).val();
         var txtcontactoId = $("<input type='text' name='txtajax_contactoid' class='loader' />").val(valor);
         var valor2 = $('#txt_Contactos_ProveedorId').val();
         var txtproveedorid = $("<input type='text' name='txtajax_proveedorid' class='loader' />").val(valor2);
         var valor3 = $('#txt_Contactos_ProveedorNombre').val();
         var txtproveedornombre = $("<input type='text' name='txtajax_proveedornombre' class='loader' />").val(valor3);

              $('#frm_ContactosLista').append(txtcontactoId);
              $('#frm_ContactosLista').append(txtproveedorid);
              $('#frm_ContactosLista').append(txtproveedornombre);

              var url = "./webservice/llenarcontactos.php";

              $.ajax({
                  type:"POST",
                  url: url,
                  data: $("#frm_ContactosLista").serialize(),
                  success: function(data){
                      $("#Mcontenido1").html(data);
                      $("#Modal_MContactos").modal();

                  }
              });

              return false;
          });

Table with the button

Modal to modify