The comparator can only do two things, it can either turn the LED on or turn it off, if it just did either of those it doesn't seem to serve any purpose, it has no controls so it's not being used as a fancy switch. Thinking it through the, the only thing that makes sense to me is that it causes the LED to flash on an off. Maybe it's like a PWM light dimmer circuit and flashes the LED on and off faster than you can see, creating a constant brightness that doesn't vary with supply voltage, this would in turn keep the range of control voltages to the VCO constant.
That seems far too complicated though.
EDIT: wrote that before I read Dino's post, sort of fits with what he said, twiddling the trimmer sets the brighness and therefore the sweeps. Still sounds too complicated though. Maybe there is something in Larry's idea.