The modified Born series method is currently one of the most efficient methods available for simulating light scattering in large inhomogeneous media. However, to achieve high accuracy, the method requires thick gradually absorbing layers around the simulation domain. Here, we introduce new boundary conditions, combining a padding-free acyclic convolution with an ultra-thin boundary layer. Our new boundary conditions minimize the wrap-around and reflection artefacts originating from the edges of the simulation domain, while also greatly reducing the computational costs and the memory requirements of the method. Our GPU-accelerated Matlab implementation is available on GitHub.