A port scan reveals Bonjour is open on my iPhone.

So I did a portscan using Scany from my iPhone and it turns out that many iPads and iPhones here have the Bonjour port open and accessible. Is there a way to shut this off? It feels like a gross security threat and really should be able to be toggled off.

Edit: Sorry, wrong forum. If moderators could move or delete the thread it would be appreciated.