Regime dependencies and Granger causal relationships between tropical and extratropical teleconnections are inferred using Bayesian structure learning. Using ERA5 data, an examination of the differences between the learned causal structures during particular phases of the Interdecadal Pacific Oscillation (IPO) are used to infer the role of the background state on interactions between the major climate teleconnections and in particular the dependence of the ENSO autocorrelation on the phase of the background state, and the role of the Madden Julian Oscillation as being key to link the extratropical tropospheric modes (PNA, NAO) and the equatorial surface ocean forced convective modes (IOD, ENSO). These relationships are presented as posterior distributions over possible graphical representations in terms of Dynamic Bayesian Network (DBN) models constructed from time series of empirical climate indices. General circulation model simulations are used to sample from a larger distribution of possible IPO periods and their phase dependencies.