From what I see, in v2 of GMaps API there was a property \"buttons\" of the InfoWindow object that one could define in a way that given InfoWindow has no close button:
google.maps.event.addListener(infowindow, 'domready', function() {
var iwOuter = jQuery('.gm-style-iw');
// Reference to the div that groups the close button elements.
var iwCloseBtn = iwOuter.next();
// Apply the desired effect to the close button
iwCloseBtn.remove()
});
As there is no option to hide this by API parameter, you have to find the element by targeting the content window and remove it.
Hope this helps :)