_marisha,
<!DOCTYPE html>
<html>
<head>
<title>Untitled</title>
<meta charset="utf-8">
<style type="text/css">
.favoritesDiv.activeFavorite {
border: 1px solid #FF0000;
}
</style>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.12.4/jquery.min.js"></script>
<script>
$(function() {
$(".favorItem").on("click", function() {
$(this).parent().addClass('activeFavorite');
})
});
</script>
</head>
<body>
<div class="put_off favoritesDiv">
<a class="favorItem text favorites buttonItem" id="1356" data-item="1356">Отложить</a>
</div></body>
</html>