I am not sure which green LED you are referring to. The module has two green LEDs, each with a different function.
You had mentioned Port-C4 (processor GPIO register bit PORTC4), which is the green LED to the left (above the red LED) can be re-programmed. In this scenario, the green LED can be reassigned as a general purpose LED. It must remain a GPIO output for the LED to operate correctly. The LED is lit when the signal is low. In other words, this LED is software programmable and is wired to processor GPIO register bit PORTC4 and wired to be lit when low.
If you meant the LED on the right (above the yellow LED), it is the network link status indicator.
In response to your question, I think you would need to review your code to see what conditions will cause the green LED (above the red LED) to light.