Undo an overridden paste in JS

I have overridden the paste event. I noticed that because the event's default behavior is prevented, it is not currently possible to undo the "paste" with Ctrl+Z.

$(this).on('paste', function (evt) {
  // Get the pasted data via the Clipboard API.
  // evt.originalEvent must be used because this is jQuery, not pure JS.
  // https://stackoverflow.com/a/29831598
  var clipboardData = evt.originalEvent.clipboardData || window.clipboardData;
  var pastedData = clipboardData.getData('text/plain');

  // Trim the data and set the value.
  $(this).val($.trim(pastedData));

  // Prevent the data from actually being pasted.
  evt.preventDefault();
});

Is there a way to override the undo functionality or do the above differently such that Ctrl+Z will work?

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