I think it is the membrane and enclosed space in the ear cup and behind it.
The influence of pads is small but certainly there, you can dampen a driver with felt in front and behind the driver.
(see
i5 review)
The problem is that people want to 'see' the driver and are of the opinion nothing should come between the driver and ear.
Audibility of this ringing depends on many factors including the music.
In most cases the instruments that are recorded have longer and more severe 'ringing' and will mask that of the driver.