Diiim,
<!DOCTYPE html>
<html>
<head>
<title>Untitled</title>
<meta charset="utf-8">
<style type="text/css">
.One {
border: 1px solid red;
}
</style>
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.5.1/jquery.min.js"></script>
<script>
$(function() {
$(".filter-wrapp").on("change", function() {
$(this).toggleClass("One", !!$(":checked", this).length)
}).trigger("change")
});
</script>
</head>
<body>
<div class="filter-wrapp"> сюда добавляем класс One
<div class="filter-content">
<ul>
<li><input type="checkbox" checked="checked"></li>
<li><input type="checkbox"></li>
</ul>
</div>
</div>
</body>
</html>