How to reduce ear splitting intercom noise?

The quick-and-dirty solution: place tape over the speaker grille. The 2" wide clear tape used for packaging/boxes provides a nice balance of muffling the sound while remaining visually unnoticeable on excessively loud childrens' toys; it'll probably do well here too.

The electrical solution: add some resistance to the speaker circuit. This could be done with a resistor added between the terminals right on the speaker, or with a resistor added in series with the speaker.

It's a bit hard to tell in the photo but I think I see the red wire from the speaker soldered to the top-left corner of the circuit board and a trace going from that point to the terminal marked 1. If that's correct then the easiest electrical hack is probably to disconnect the green wire and insert a resistor there.

The resistor could be a variable type ("potentiometer") like this 200 ohm Bourns 3386X-1-221LF

or it could be a through-hole fixed-value type that looks similar to this

The potentiometer is nice because you can adjust its resistance (and therefore the speaker volume) by turning the dial. You'll almost certainly have to solder wires to attach to those leads though. The through-hole resistor would be easy to install (no soldering) but you'll have to experiment to find the right value. Fortunately resistor kits with a variety of values can be had at low cost. Something in the range of 20-150 ohms will probably put the speaker volume where you'd like it.

If you find that this hack makes the voices in the intercom inaudible then you could add a momentary normally open push-button switch. The switch would be wired across the resistor so that when pushed the resistor is bypassed and the speaker goes to full/normal volume.

Over-engineered solution:

1. Get a programmable timer switch. This contains a relay that will switch on/off when you program it to do so.

2. Cut the red speaker wire and insert the relay in series with the speaker. Set the timer so the relay is off at night, which basically disconnects the speaker.

3. Sleep.

You can put a 1000 ohms 1 Watt resistor across the relay terminals. So when the relay is on, it shorts the resistor and the speaker is at full volume, and when the relay is off the resistor is in series with the speaker, like so:

Notes:

Sound perception is not linear, so if you put say a 100 ohm resistor you'll get about 3x less voltage across the loudspeaker, but it won't sound 3x less loud... it will sound a bit less loud. Therefore, more ohms. Resistors are cheap, you can buy several values.

You should not buy a switched socket because that will output mains voltage. You need a timer switch which lets you access the relay contacts, like this one. Many different models are available. I selected one that is powered from 12V, that's a good idea if you don't want to mess with mains voltage, just use any old 12V wall wart you have lying around.

This will also attenuate the speaker when talking to people though. That's why I thought about the timer, so the thing stays more or less functional during the day.

Of course, you could use a manual switch to make a 2-position volume control, but then you forget to turn it down at night and some drunk hooligans ring all the doorbells at 2AM...