I'm not up with firesticks but, I would assume they could try using an update to block these so it would be better to ensure the stick isn't set for auto-update and refuse when requested.

Read the same, or similar, for months.  There's settings that you can change to prevent Amazon seeing what apps you're using.  If you think how many Firesticks there are it's close to an impossible task As far as I've been made aware they have no right to enter your property so a polite "feck off" would suffice. 

Full list of 'dodgy firesticks' crackdown areas as Amazon warns users It seems Amazon are about to do a purge on the dodgy firesticks from this article dated yesterday.