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aynasız = without a mirror (literal), slang for police, cop

kökeni şudur: eskiden her erkek vatandaş cebinde ayna ve tarak taşırmış, bıyığını tarayıp düzgün tutmak için. polislerin bıyık bırakması yasak olduğundan bu aksesuarları taşımazlarmış. (ekşi sözlük)

The origin of the word: In the old times every man carried a comb and mirror in his pocket in order to comb and keep his moustache tidy But it was forbidden for police oficers to grow a moustache so they didn´t carry these accessories.

So that is why people called them "aynasız(without a mirror)"

I think they mocked them this way because it must be very weird for a man to not to grow a mustache in those times.