Context. Although there is currently a debate over the significance of the claimed large-scale anomalies in the cosmic microwave background (CMB), their existence is not totally dismissed. In parallel to the debate over their statistical significance, recent work has also focussed on masks and secondary anisotropies as potential sources of these anomalies. Aims. In this work we investigate simultaneously the impact of the method used to account for masked regions as well as the impact of the integrated Sachs-Wolfe (ISW) effect, which is the large-scale secondary anisotropy most likely to affect the CMB anomalies. In this sense, our work is an update of previous works. Our aim is to identify trends in CMB data from different years and with different mask treatments. Methods. We reconstruct the ISW signal due to 2 Micron All-Sky Survey (2MASS) and NRAO VLA Sky Survey (NVSS) galaxies, effectively reconstructing the low-redshift ISW signal out to z similar to 1. We account for regions of missing data using the sparse inpainting technique. We test sparse inpainting of the CMB, large scale structure and ISW and find that it constitutes a bias-free reconstruction method suitable to study large-scale statistical isotropy and the ISW effect. Results. We focus on three large-scale CMB anomalies: the low quadrupole, the quadrupole/octopole alignment, and the octopole planarity. After sparse inpainting, the low quadrupole becomes more anomalous, whilst the quadrupole/octopole alignment becomes less anomalous. The significance of the low quadrupole is unchanged after subtraction of the ISW effect, while the trend amongst the CMB maps is that both the low quadrupole and the quadrupole/octopole alignment have reduced significance, yet other hypotheses remain possible as well (e. g. exotic physics). Our results also suggest that both of these anomalies may be due to the quadrupole alone. While the octopole planarity significance is reduced after inpainting and after ISW subtraction, however, we do not find that it was very anomalous to start with.