There is no easy way to do it, but you can change the image with CSS. Technically, CSS adjustments are considered custom coding & are not covered by support, but I was curious to see if I could figure out a way to do what you want without needing to edit core theme or framework files, and I believe I have found a solution.
If you add the following code to the end of the theme's style.css file, it'll replace the mobile menu icon with the "S5" favicon image from the theme. To use a custom image, just change the URL, and adjust the sizes as needed to make it look right:
content: none !important;
width: 25px !important;
height: 25px !important;
background-size: 25px auto;