Transistor Based LED Switching Circuit Design
200R * 10 nF = 2us  reduces the radiated noise on a cable for the SW band somewhat if it was nearby the radio on a weak channel.  f=0.35/tR is the -3dB point. For 10~90% thus T ~3us.

Otherwise it is not needed.

In most cases your CMOS 50 Ohm driver can drive the Green LED directly with same or a resized Rs value. The ARM driver is closer to 25 Ohms. With cathode to 0V or Anode to Vdd.

EDIT 2:20pm.
The added schematic imposes no requirement for the LED cap. 

So it was probably added for “insurance” (lack of analysis) of pop noise reduction on AM/SW radio interference. Considering the low current and low inductance of cable, it is useless otherwise.  However poor wiring might cause some crosstalk.