#1. Add a non-clickable image to the mobile menu overlay
You can use this code to Custom CSS box. Replace Pixabay with your desired image url
[data-folder="root"] .header-menu-nav-wrapper:before {
content: "";
background-image: url(https://cdn.pixabay.com/photo/2018/07/10/21/53/tournament-3529744_1280.jpg);
display: block;
width: 200px;
height: 150px;
background-size: contain;
background-repeat: no-repeat;
background-position: center;
margin: 0 auto;
position: relative;
}

Result:

#2. Add a clickable image to the mobile menu overlay
Use this code to Code Injection Footer
<script src="https://assets.squarewebsites.org/lazy-summaries/lazy-summaries.min.js"></script>
<script>
$(document).ready(function(){
$('<a class="custom-img" href="https://squarespace.com"><img src="https://cdn.pixabay.com/photo/2018/07/10/21/53/tournament-3529744_1280.jpg"/>').insertBefore('.header-menu-nav-wrapper');
});
</script>
<style>
a.custom-img img {
width: 250px;
padding-left: 6vw;
margin-left: 4vw;
}
</style>

Result:
