Hi,
The dc_amplifier_offset_control is a somewhat finer detail of the circuit which is mentioned in the text but unfortunately NOT shown on the schematic.
The dc_amplifier_offset_control is responsible for providing an output from the DC amplifier when there is zero output from the low pass filter, as required by the voltage controlled oscillator to provide a nominal output frequency. In many cases this frequency will be around the center of the range of the VCO. Thus, we may see a positive deviation from the nominal output offset or a negative deviation from the nominal output, providing both frequencies above and below the nominal VCO output.
This function may also be relegated to the VCO itself however, or partly so and partly via an actual output offset voltage.
This is probably too detailed for this particular paper anyway, so they didnt want to place too much significance on it and in doing so miss the main points. For example, with a zero offset we dont even have to consider it except to note that it is zero
So they mention it more casually in passing so most people wont worry about it too much for now. In a practical circuit we'd have to think about it of course.
It would have helped if they drew a line showing exactly what part of the circuit the offset was affecting, but again they probably didnt want to focus too much on that little detail. For example, they also didnt draw the power supply leads or bypass capacitors, but we assume they are there and working in a real circuit.
We could argue that is true but then again they didnt actually mention the power supply in the text while they did mention the offset, so this paper was probably written by someone who forgot what it was like to be curious by nature.