Experiments on DIII-D confirm that the tritium breeding test blanket modules (TBMs) in ITER will lead to a decrease of the plasma rotation in H-modes [M.J. Schaffer, et al., Nucl. Fusion 51 (2011) 103028]. Moreover, they suggest that long-wavelength correction fields applied with non-axisymmetric saddle coils will only be able to ameliorate a fraction of such a rotation reduction. The new finding obtained in rotating H-modes with parameters similar to the ITER baseline scenario contrasts previous experiments, which showed that saddle coils are very effective in restoring resilience to locked modes in L-mode plasmas. The experiments use a TBM mock-up coil that has been especially designed to simulate the error field induced by the ferromagnetic steel of a pair of TBMs in one ITER port. The n = 1 error field correction (EFC) is applied with a set of non-axisymmetric saddle coils (I-coil), whose currents are optimized in the presence of the TBM mock-up field using a newly developed non-disruptive technique that maximizes the angular momentum. However, a test of the effectiveness of the TBM EFC yields that the optimized EFC can only recover approximately a quarter of the ~20% rotation decrease attributed to the TBM error field. An alternative criterion to evaluate EFC has been its effectiveness in canceling the n = 1 plasma response to the field error. Plasma response measurements in the TBM experiment show that the I-coil can indeed cancel the magnetic measurements of the n = 1 plasma response to the TBM mock-up field. The required currents agree within the uncertainties of the estimates with the currents that maximize the angular momentum. The contrast between the limited effectiveness of n = 1 EFC in rotating H-modes and their ability to recover a low locking density in L-mode plasmas shows that the components of the non-axisymmetric field that brake the plasma at higher values of beta or higher rotation differ from the components that are responsible for the field penetration in low density L-modes.