You will need to customize the class framework/widgets/mo-contact-info-widget.php. Will need to know the basics of how widgets work although code should be fairly easy to follow.
I would strongly recommend you try using a plugin like contact form 7 instead which lets you build custom forms with ease. You can paste the shortcodes for the forms created in CF7 into any text widget.
Looks like I misunderstood your query. If you want to customize the contact info widget, I would recommend you grabbing the HTML generated by this widget and putting the same into a text widget. You can then customize this simple piece of HTML code. No need to mess with the widget code for this.