I might be missing something in your question here... but from what I can gather, by using the subtract method this should be what you're looking to do:
var timeStr = "00:03:15";
timeStr = timeStr.split(':');
var h = timeStr[1],
m = timeStr[2];
var newTime = moment("01:20:00 06-26-2014")
.subtract({'hours': h, 'minutes': m})
.format('hh:mm');
var str = h + " hours and " + m + " minutes earlier: " + newTime;
console.log(str); // 3 hours and 15 minutes earlier: 10:05
$(document).ready(function(){ _x000D_
var timeStr = "00:03:15";_x000D_
timeStr = timeStr.split(':');_x000D_
_x000D_
var h = timeStr[1],_x000D_
m = timeStr[2];_x000D_
_x000D_
var newTime = moment("01:20:00 06-26-2014")_x000D_
.subtract({'hours': h, 'minutes': m})_x000D_
.format('hh:mm');_x000D_
_x000D_
var str = h + " hours and " + m + " minutes earlier: " + newTime;_x000D_
_x000D_
$('#new-time').html(str);_x000D_
})
_x000D_
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>_x000D_
<script src="https://cdnjs.cloudflare.com/ajax/libs/moment.js/2.9.0/moment.min.js"></script>_x000D_
_x000D_
_x000D_
<p id="new-time"></p>
_x000D_