If you're planning to show them again later, you could add the 'style="display:none"' to whatever creates the HTML you're inserting (the function behind /myurl, in other words), then you can simply show these elements later in a deferred listener, such as the ones created by the on() method.
// /myurl => '<input type="text" class="foo" style="display:none">'
// later, in the combined page
document.on('click', '.some-control', function(evt, elm){
evt.stop();
$$('.foo').invoke('show');
});
That's a fairly broad selector, you could do something much more specific using next and previous or an id selector instead. The point of the on() method is that the contents of its closure are not evaluated until the event happens, so you can rely on everything that matches the selector being found when it is evaluated, whether it was there at page load or was added later.
If you just want to hide the things that are being added to the page, and you want a completely agnostic method, you can try this:
document.on('DOMSubtreeModified', function(evt){
$$('.some-selector-here').each(function(elm){
if(elm.visible()) elm.hide();
});
});
That will fire each time the page is modified, so you can test and hide things as they are added if they match your inner selector.