How to deauthorize an iPhone without iTunes?
You should explicitly deauthorize it. The standard way is to use iTunes.

But if you do not want to install or use iTunes, you can get Apple Support to help you:


Go to the Apple iTunes Support page
Click on the Contact iTunes Store support link (click OK when it prompts you about redirecting you to another page)
This currently takes you to the What's happening with iTunes? page
Click the Account Management box to open up further options
Click the iTunes authorization or de-authorization link
Choose how you would like help - the current options are for Apple to call you or to schedule a call back from Apple or email Apple Support
Provide the details of the Apple ID and the device in the request for deauthorization