We study the contributions to the relativistic Fe K-alpha line profile from higher order images (HOIs) produced by strongly deflected rays from the disc which cross the plunging region, located between the innermost stable circular orbit (ISCO) radius and the event horizon of a Kerr black hole. We investigate the characteristics features imprinted by the HOIs in the line profile for different black hole spins, disc emissivity laws, and inclinations. We find that they extend from the red wing of the profile up to energies slightly lower than those of the blue peak, adding similar to 0.4-1.3 per cent to the total line flux. The contribution to the specific flux is often in the similar to 1 to 7 per cent range, with the highest values attained for low and negative spin (a less than or similar to 0.3) black holes surrounded by intermediate inclination angle (i similar to 40 degrees) discs. We simulate future observations of a black hole X-ray binary system with the Large Area Detector of the planned X-ray astronomy enhanced X-ray Timing and Polarimetry Mission (eXTP) and find that the Fe K-alpha line profiles of systems accreting at less than or similar to 1 per cent the Eddington rate are affected by the HOI features for a range of parameters. This would provide evidence of the extreme gravitational lensing of HOI rays. Our simulations show also that not accounting for HOI contributions to the Fe K-alpha line profile may systematically bias measurements of the black hole spin parameter towards values higher by up to similar to 0.3 than the inputted ones.