Why does AngularJS ignore $scope field change?

I want my modal dialog to be blurred while Stripe Checkout is open above it, but for some reason it stays blurred even after I've closed the secondary modal.

It's best to try it in a sample plunkr

Use card "4242 4242 4242 4242" to test, with any future expiry date and CCV. Blur must disappear once stripe window is closed, but it doesn't for some reason.

This is all basic stuff and I've been using angular for at least 3 years now, just cannot figure out where is the bug this time.

Here's JS code from the aforementioned example:

angular.module('ui.bootstrap.demo', ['ui.bootstrap']);
angular.module('ui.bootstrap.demo').controller('ModalDemoCtrl', function ($scope, $modal, $log) {

  $scope.open = function () {
    var modalInstance = $modal.open({
      templateUrl: 'myModalContent.html',
      controller: 'ModalInstanceCtrl',
    });
  };
});


angular.module('ui.bootstrap.demo').controller('ModalInstanceCtrl', function ($scope, $modalInstance) {

  // Text is not blurred by default.
  $scope.isbusy = false;
  console.log('dlg scope is ', $scope.$id);

  $scope.pay = function () {
      // Blur the parent dialog.
      $scope.isbusy = true;
      console.log($scope.$id, ' marked as busy');

      var handler = StripeCheckout.configure({
          key: 'pk_test_hh0HjBRRI5Ak793gMgLEZEVN',
          token: function(token) {
              // Remove blur effect.
              $scope.isbusy = false;
              console.log($scope.$id, ' marked as NOT busy');
          },
          closed: function() {
              // Remove blur effect even if user clicks close.
              $scope.isbusy = false;
              console.log($scope.$id, ' marked as NOT busy');
          }
      });

      handler.open({
          name: 'Enter Your Card Details',
          email: '[email protected]',
      });

  };

});