While Aurora's answer states that the status LEDs cannot be toggled by the user, it is not completely clear whether only the manufacturer firmware does not support this toggling or if the LEDs are simply hardwired and can thus not be controlled by any firmware at all. If they are connected to GPIO pins of the controller, a custom firmware could enable you to switch them of or even use PWM to dim them down. How to "jailbreak" the system is described here.
If the LEDs cannot be toggled from the system and are hardwired it is still possible to tweak the hardware. The LEDs in question are D8..D11 on the PCB. Opening the case (and voiding the warranty and all) you could try to trace the connections of these LEDs that will eventually lead to some resistors. Removing those resistors and replacing them with higher values will reduce the current and thus the luminous flux.
If you cannot find the resistors and just want to disable the LEDs you can simply remove them... or block the lightpath inside the housing (covering the LEDs). This way the device will at least keep a pristine look from the outside.
Unfortunately, this is not possible to be done from the available pictures only, you'll have to open it and figure it out (you'll need a meter).