var oldFunc = thirdParty.theirFunc;
thirdParty.theirFunc = function(){
    oldFunc();

    // alert myself of the change.
    myDomChangedFunction();
};

.ajaxComplete()

MutationObserver

// select the target node
    var target = document.getElementById('some-id');

    // create an observer instance
    var observer = new MutationObserver(function(mutations) {
    mutations.forEach(function(mutation) {
        console.log(mutation.type);
    });
    });

    // configuration of the observer:
    var config = { attributes: true, childList: true, characterData: true };

    // pass in the target node, as well as the observer options
    observer.observe(target, config);

    // later, you can stop observing
    observer.disconnect();