Electronic – Horn antenna for radar sensor

From the shape of the depicted plate, that is an E-field capacitive iris to be inserted in a specific physical location in the waveguide between the electronics and the antenna. If the waveguide is a transmission line, the capacitive iris is basically a capacitor shunting the transmission lines at that physical distance along the line. Typically this is done to create better impedance matching such as to cancel an "inductive" type of mismatch effect so that the transmitter / receiver is better impedance matched to the antenna at a particular operational frequency. They likely wouldn't have included it if it were not meant to be used and make an improvement in the matching. The only reason it wouldn't be used is if there was an alternative type of antenna that it was to be used with or if there's a very different frequency band option that the transceiver is able to be used with such that it is to be used in one configuration and not the other. Typically you'd just use it as is. Besides matching improvement it could also help to filter out out of band interfering signals either from propagating from the antenna to the transceiver or from the transceiver to the antenna. You wouldn't likely see much improvement in a short range bench test but if you were operating at long range near the limit of the equipment such that you might notice a 1dB or so improvement then you'd more likely notice a difference.

It could also be useful to create a known and purposeful mismatch or to increase the resonant cavity Q by decreasing its coupling to the antenna if it were useful in the desired configuration to get a little more of the GP's own signal reflected/resonated back into the GP unit cavity though that depends on the unit's design and purpose.

Edit -- on second look since that has a capacitive E-field gap ("capacitor") as well as "rounded" loops ("inductors") at the H-field inductive ends, and it looks to be in a conductive (copper, brass, maybe silver plated) plate that plate's iris also could work like an LC resonant lumped element filter so it could be useful in that capacity to provide signal bandwidth filtering as well as the above possible explanations. The Q and center frequency precision could be relatively high, maybe in the hundreds or less by my guess.
That could help get the GD oscillations going, provide Q related tuning / selectivity, and help set the S11, S21 in the transceiver's band according to the above matching and resonance concerns.

For a compound box antenna the formula is similar and this might be useful: -

Obviously they are not using A and B to denote the aperture dimensions but, I suspect that "r" is going to be exactly the same i.e. distance between centre of aperture and measurement point.