I would have expected the transmitter to be the stationary unit that applies the signal to the fence, and the mobile device on the dog's collar to be the receiver that detects the signal and electrocutes the poor animal each time it approaches the fence.
An oscilloscope applied to the output of the transmitter will show its waveform, so you can determine the frequency and possibly the type of encoding. From which you can design a receiver circuit for that frequency. Or just dismantle the receiver and copy the circuit.
The receiver in your key fob could be a tuned circuit that receives the transmitted frequency, with a suitably programmed microcontroller to identify the encoding and activate the high voltage shock module.
Then you could get an electric shock from your key fob each time you go near the fence, and you would know exactly what the poor dog suffers, and why it makes that strange noise.
YEEEE-OW-OW-OW-BOW-WOW-WOW-WOW ! ¦-0