I think the balun and the 180deg delay is there simply to reject the dither signal (its fixed frequency so cancellation should be good)
No, the dither signal is removed in the digital down conversion process.
The dither is supposedly just added to the input signal to increase the dynamic range after processing.
If that addition is done directly to the output signal of the LNA in front of the VCO then I suspect it could have unwanted non linear effects and that this would cause unwanted mixing to happen in the LNA.
So I view the balun and the strip lines as a trap for VCO signals so they can not propagate backwards to the LNA in the input.
Alternatively it might be useful to not have VCO emissions leaking out of the coax connector on the frontpanel when the amplifier is bypassed.
Edit: never mind that theory about rejection, on second looks the delay line is just the balun for the signal from the VCO to make it differential (the ADC wants it like that)
Notice how the signal takes of on an inner layer up and to the left just after the balun just in the same place where it met the signal from the VCO.