Never used a satellite dish, but in school we once made reflectors using paper mache over half a large (18") balloon and they worked pretty well, we could pick up what the teacher was saying in the classroom across the quad
I have used satellite TV dish to record bird songs at very high distance (100 m) Works very well, but unusable at low frequencies. Some equalization can be implemented in order to correct the increasing efficiency with the frequency. The position of the microphone must be carefully adjusted by extensive tests, because it's not possible to simply put the microphone instead of the LNA, which phase center is generally not well known.
An umbrella with the inside surface coated with a more sound-reflective material e.g. varnish etc might be suitable. You also have a central pole to attach the microphone to, though it gets in the way a bit.
The increasing efficiency with frequency of parabolic reflector is normal at audio frequencies, as well as radio frequencies. But this is true only for a near strictly parabolic reflector (as SATV dish) not for umbrella or such approximate reflector, which exhibit a maximum efficiency for a particular wavelenght, depending of the actual incurvated form.
SATV dishes are computed for max efficiency at 4 or 5 GHz (in the USA) i.e. about 3 inches wavelenght. I suppose that the max efficiency occurs in the range 2...6 kHz for audio frequencies. European SATV dishes are computed for max efficiency at 12 GHz, requiring a more precise production, and the max efficiency occurs at about 6...15 kHz, giving a noticeable presence effect with a good electrostatic microphone (I use B&K 4133).
I guess that the lifting response makes it better for eavesdropping on neighbours then.
I thought that a parabola is a parabola and effective at all frequencies, and the low frequency gain dependant on the area of the reflector.
I mostly posed the question for interest sake, but if I can get hold of a disused dish I am keen to try the experiment.