Try wrapping the $(this).parent() into an jQuery object like $($(this).parent()) I often find the need to do this to make sure I have a valid jquery object. From there you should be able to get a hold of the parents parent, or using the prev() perhaps.
Closest works by first looking at the current element to see if it matches the specified expression, if so it just returns the element itself. If it doesn't match then it will continue to traverse up the document, parent by parent, until an element is found that matches the specified expression. If no matching element is found then none will be returned.
If you have any sort of id/class for the parent, you can use parents() but that will give you all parents up to the < body > unless you filter() or stop it some other way like