Try this:
<div class="rmz-srchbg">
<input type="text" id="globalsearchstr" name="search" value="" class="rmz-txtbox">
<input type="submit" value=" " id="srchbtn" class="rmz-srchico">
<br style="clear:both;">
</div>
<script>
$(function(){
$('#globalsearchstr').on('focus mouseenter', function(){
$(this).parent().css("background", "url(/images/r-srchbg_white.png) no-repeat");
});
});
</script>
