The story
From parrot (“(aviation, slang) transponder”). “Parrot” was the British codename for the identification friend or foe system on World War II aircraft which used transponders.
Etymology from Wiktionary, CC BY-SA 4.0.
strangle the parrot
stran·gle the par·rotToday it means: To switch off the transponder, for example, because it is interfering with the radar system. Full definition →