The control pin is connected to an LED and a resistor in series. The forward voltage on the LED is typically 1.2V and the resistor is 392 Ohms. So depending on what voltage your Arduino digital output is switching,
Current = (V - 1.2)/392
If it's a 5V digital output, the current will be 9.6mA, and if its a 3.3V digital output, the current will be 5.4mA.
Interestingly enough, we should probably have this included on our spec sheet for the device. I'll see what I can do to get it added there.
Additionally, I think you are misunderstanding the 40mA limit that Arduino's have on the pins. This applies to each digital output, and not the ground pins. So each digital output will be able to source or sink 40mA.
In short, you don't even need to worry about the current going through the ground pins.