Quantum Monte Carlo (MC) simulations of the 2D S=1/2 Heisenberg antiferromagnet (AFM) with a vacancy and an applied magnetic field [1] showed that the characteristic decay length of the alternating magnetization around the defect displays an unexpected maximum in the neighborhood of the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature. Given the role played in the BKT transition by vortex excitations, we investigated their contribution to the alternating-order behaviour, showing that isolated vortices modulate the parameters entering the effective model introduced in [1]: the temperature dependence of the vortex population allows us to explain the observed behaviour of the alternating-order decay length. We support such conclusions with MC simulations of the classical AFM, which also reveal some differences between the quantum and the classical model.