Hi, I downloaded a wordpress plugin called jQuery Smooth Scroll to have a smooth scrolling on my webpages to anchors and also have a scroll up feature.

The plugin displays an arrow image (png) to scroll all your way up to the page when you click on it. This arrow image appears after scrolling down the page a bit (I set it to 2000px) and everything is working fine... except that even though the arrow isn't displayed, the scroll to top link is still there so you can click on the area and scroll to the top even though you can't see it.I'm trying to get rid of this hidden area link when the png fades out.

Here's a portion of the code I think is relevant.
/* Smooth Back to Top, Get This functionality from: http://wordpress.org/extend/plugins/cudazi-scroll-to-top/ */

jQuery(function($) {
	// When to show the scroll link
	// higher number = scroll link appears further down the page	
	var upperLimit = 2000; 
	// Our scroll link element
	var scrollElem = $('a#scroll-to-top');
	// Scroll to top speed
	var scrollSpeed = 500;
	// Show and hide the scroll to top link based on scroll position	
	$(window).scroll(function () { 			
		var scrollTop = $(document).scrollTop();		
		if ( scrollTop > upperLimit ) {
			$(scrollElem).stop().fadeTo(300, 1); // fade back in			
			$(scrollElem).stop().fadeTo(300, 0); // fade out

	// Scroll to top animation on click
		$('html, body').animate({scrollTop:0}, scrollSpeed); return false; 

I think the rest of the code is only related to anchors links.
Thanks in advance,