You can figure out where the item is in the nginx cache directory and delete it. But that is complicated by the fact that your app and nginx run as different users. Or you can send a specially crafted HTTP request to nginx assuming you have some kind of backdoor proxy_cache_bypass setup. But that's ugly too. You either have a race condition, or you have to hang your app's response until the invalidation request completes.
If there's another way to evict an item from the cache, I'm all ears.