Nevertheless you are making a mistake somewhere, the code for the buttons is contained in the span tag with the class clsSwitch, giving it a css style of display:none will hide it without a doubt.
If for some reason you cannot make it work you can try deleting the code on lines 4-6 from the template entirely.
<span class="clsSwitch">Switch View <a href="javasc*ript:showGrid('<?php echo $uniqid; ?>','gridview','listview');" title="Grid View"><img id="Img1" name="Img2" class="view" src="<?php
echo $baseurl."modules/mod_virtuemart_featureprodgrid/assets/pro_img1gallery.jpg"; ?>" width="15" height="13"/>
</a><a href="javasc*ript:showGrid('<?php echo $uniqid; ?>','listview','gridview');" title="List View"><img id="Img2" name="Img1" class="view" src="<?php echo $baseurl."modules/mod_virtuemart_featureprodgrid/assets/pro_img2_normal.jpg"; ?>"/></a></span><br /><br />