Userscripts.org

The calendar count shows you how many events you have that are happening today. It can't really be "cleared" (without removing an event, obviously).
I'd love changing it so that it shows you events that are happening in the rest of the day (events that are "today", but past "now"), but that would require knowing what timezone you're on, and that is not something that I can access easily from within a userscript. Hopefully, once I finish converting the script into an extension, that will change.

You will have to modify the _updateCountBox() method.

Something like this might work:

_updateCountBox: function (id, count, color, background) {
		$(id).fadeOut(400, function() {
			if (count > 0) $(this).html(count).css({'color': color, 'background-color': background}).fadeIn(300);
		});
	}

Note: This is untested, but it _should_ work as-is.

Calendars on Google Calendar are poorly implemented. Working with the API is even worse. That said, it IS on my to-do list, so it will be possible at some point. IF they had a "today" feed available via API, that would save a ton of time for developers such as myself, but sadly that is not the case.