We assess the effect of the European design of the pebble-bed helium-cooled test blanket modules (TBM) on fast ion power loads on ITER material surfaces. For this purpose, the effect of not only the TBMs but also the ferritic inserts (FI), used for mitigating the toroidal field ripple, were included in unprecedented detail in the reconstruction of the 3-dimensional magnetic field. This is important because, due to their low collisionality, fast ions follow the magnetic geometry much more faithfully than the thermal plasma. The Monte Carlo orbit-following code ASCOT was used to simulate all the foreseen operating scenarios of ITER: the baseline 15 MA standard H-mode operation, the 12.5 MA hybrid scenario, the 9 MA advanced scenario, and the half-field scenario with helium plasma that will be ITER's initial operating scenario. The effect of TBMs was assessed by carrying out the simulations in pairs: one including only the effect of ferritic inserts, and the other including also the perturbation due to TBMs. Both thermonuclear fusion alphas and NBI ions from ITER heating beams were addressed. The TBMs are found to increase the power loads, but the absolute values remain small. Neither do they produce any additional hot spots.