Sure. And first my apologies for taking so long to reply. Got a bit sidetracked.
Well, for dynamic headphones, which don't have a nice flat, resistive impedance curve, it can effect frequency response. But for orthos, which is the subject of this thread, the concept of "damping factor" isn't really relevant. The impedance curve of orthos is flat and virtually purely resistive so the resistor's only effect is signal attenuation.
No, it's not to match the impedance of the headphone, but rather to allow the headphone to see a lower output impedance from the amp than it would see if just using a series resistor.
Let's say you're using a 100 ohm series resistor. Then the impedance seen by the headphone would be 100 ohms. But add a 10 ohm parallel resistor and now the headphone sees an impedance of 100 ohms in parallel with 10 ohms which comes to about 9 ohms.
Of course you could do all the attenuation with just a parallel resistor, but it may end up being of such a low value that it could end up having to dissipate a fair amount of heat. So a series/parallel pair is a good compromise to give you a lower output impedance while not having to dissipate much heat.
Well, as I said above, the purpose of the parallel resistor isn't to match the headphone impedance but rather to have the headphone see a sufficiently low output impedance that it won't have a significant effect on its frequency response.