Righty, sorry for the late reply.
I had a quick look and whilst I can't be certain - I can't see under the IC, it looks to be a two stage amplifier. With "R1", "R2" and "R3" being the input resistor to an inverting opamp.
Changing either the input resistor, or the feedback resistor in an inverting opamp circuit will change the gain, measuring the ratio of feedback to input resistances will give you the actual voltage gain of that
opamp. The fact that the only real silkscreen on that are the labels R1-3, tells me thats the gain setting resistor - with non populated footprints for placing different value resistors.
On the right of the dual opamp is the resgulator, and a few passives which, to me, look like a bias network - creates a mid-rail voltage (could be VCC/2, but not always) - that allows the opamp to work with a single supply. Above that is the mic bias supply, that provides a DC bias to the electret mic element, looks like that has a 6.8V Zener to cap it at that voltage, and to protect it from high voltage transients.
It's hard to see if that second opamp is inverting or not, since I can't see if the input to that opamp is conencted to the inverting, or non inverting input.
I've labelled up some pointers on your image. Take tihs with a pinch of salt - I didn't spend too long looking at it so I could be wrong, but I woudl start by measuring those feedback and input resistors on the image. The unpopulated footprints could have wires soldered to them, with a resisotr wolders to it, which puts a resistor in parallel with the input resistors, reducing its value - and increasing the gain.
If you want to reduce the gain, then themadhippy's suggestion of a potentiometer on the output - just like a volume control - woudl be easiest