Zener diode protection is basically useless.
Voltage limit for an Arduino pin is not 5volt.
It's VCC + 0.5volt (and GND - 0.5volt).
If the Arduino is off, then pin limit is 0.5volt, making a 5.6volt zener useless.
Arduino pins have internal clamp diodes. They might be ok for occasional protection if current is limited to 1mA.
External schottky clamp diodes (with current limiting resistors) could be another option.
Tell us what you have connected to the Arduino pins.
And why you connect this to three pins.
You might not need all of this.
Leo..