It is a well-known fact that the presence of a massive perturber interacting with a population of minor bodies following very eccentric orbits can strongly affect the distribution of their nodal distances. The details of this process have been explored numerically and its outcome confirmed observationally in the case of Jupiter, where a bimodal distribution of nodal distances of comets has been found. Here, we show evidence for a possible bimodal distribution of the nodal distances of the extreme trans-Neptunian objects (ETNOs) in the form of a previously unnoticed correlation between nodal distance and orbital inclination. This proposed correlation is unlikely to be the result of observational bias as data for both large semimajor axis Centaurs and comets fit well into the pattern found for the ETNOs, and all these populations are subjected to similar background perturbations when moving well away from the influence of the giant planets. The correlation found is better understood if these objects tend to avoid a putative planet with semimajor axis in the range of 300-400 au.