Point-by-point (PbP) inscription of fiber Bragg gratings using femtosecond laser pulses is a versatile technique that is currently experiencing significant research interest for fiber laser and sensing applications. The recent demonstration of apodized gratings using this technique provides a new avenue of investigation into the nature of the refractive index perturbation induced by the PbP modifications, as apodized gratings are sensitive to variation in the average background index along the grating. In this work we compare experimental results for Gaussian- and sinc-apodized PbP gratings to a coupled-mode theory model, demonstrating that the refractive index perturbation induced by the PbP modifications has a negative contribution to the average background index which is small, despite the presence of strong reflective coupling. By employing Fourier analysis to a simplified model of an individual modification, we show that the presence of a densified shell around a central void can produce strong reflective coupling with near-zero change in the average background index. This result has important implications for the experimental implementation of apodized PbP gratings, which are of interest for a range of fiber laser and fiber sensing technologies.