Longer explanation.
You created a series circuit with the TVS. When the TVS conducts- now that current is going through a dropping resistor and LED- neither of which can handle much current or spike in voltage.
Net effect- the LED blinks when a spike is conducted- until it blows the LED and then the TVS isn't doing jack squat. It wasn't doing anything useful before in the circuit for protection and now less than nothing when your circuit blows the LED.