Google Apps Script which cleans the Table of Content from unwanted headings.

clean-toc.gs

/**
 * Creates a menu entry in the Google Docs UI when the document is opened.
 *
 * @param {object} e The event parameter for a simple onOpen trigger. To
 *     determine which authorization mode (ScriptApp.AuthMode) the trigger is
 *     running in, inspect e.authMode.
 */
function onOpen(e) {
  DocumentApp.getUi().createAddonMenu()
      .addItem('Clean Table of Contents', 'cleanToC')
      .addToUi();
}

/**
 * Runs when the add-on is installed.
 *
 * @param {object} e The event parameter for a simple onInstall trigger. To
 *     determine which authorization mode (ScriptApp.AuthMode) the trigger is
 *     running in, inspect e.authMode. (In practice, onInstall triggers always
 *     run in AuthMode.FULL, but onOpen triggers may be AuthMode.LIMITED or
 *     AuthMode.NONE.)
 */
function onInstall(e) {
  onOpen(e);
}

/**
* Remove unwanted elements from ToC.
* Takes some time...
*/
function cleanToC() {

  var body = DocumentApp.getActiveDocument().getBody();
  var toc = body.findElement(DocumentApp.ElementType.TABLE_OF_CONTENTS).getElement().asTableOfContents();

  for (var i = toc.getNumChildren() - 1; i >= 0; i--) {
    var tocElem = toc.getChild(i);
    var level;
    var heading;
    
    // Search for the text of the ToC element.
    var searchText = tocElem.getText();
    // This loops through all elements of the document.
    // Time to go get some coffee.
    for (var j = 0; j < body.getNumChildren(); j++) {
      var bodyElem = body.getChild(j);
      if(bodyElem.getType() == DocumentApp.ElementType.PARAGRAPH) {
        var par = bodyElem.asParagraph();
        if(par.getText() == searchText) {
          level = par.getHeading();
        }
      }
    }

    // Enter all headings you wanna keep!
    if(level !== DocumentApp.ParagraphHeading.HEADING2) {
      tocElem.removeFromParent();
    }
  }
}