Context. The recent claims of g-mode detection have restarted the search for these potentially extremely important modes. The claimed detection of g modes was obtained from the analysis of the power spectrum of the time series of round-trip travel time of p modes. Aims. The goal of this paper is to reproduce these results on which the claims are based for confirming or invalidating the detection of g modes with the method used to make the claims. Methods. We computed the time series of round-trip travel time using the procedure given in Fossat et al. (2017, A&A, 604, A40), and used different variations of the times series for comparison. We used the recently calibrated GOLF data (published in Paper I) with different sampling, different photomultipliers, different length of data for reproducing the analysis. We also correlated the power spectrum with an asymptotic model of g-mode frequencies in a similar manner to Fossat and Schmider (2018, A&A, 612, L1). We devised a scheme for optimising the correlation both for pure noise and for the GOLF data. Results. We confirm the analysis performed in Fossat et al. (2017) but draw different conclusions. Their claims of detection of g modes cannot be confirmed when changing parameters such as sampling interval, length of time series, or photomultipliers. Other instrument such as GONG and BiSON do not confirm their detection. We also confirm the analysis performed in Fossat and Schmider (2018), but again draw different conclusions. For GOLF, the correlation of the power spectrum with the asymptotic model of g-mode frequencies for l = 1 and l = 2 show a high correlation at lag=0 and at lag corresponding to the rotational splitting ν l , but the same occurs for pure noise due to the large number of peaks present in the model. In addition, other very different parameters defining the asymptotic model also provide a high correlation at these lags. We conclude that the detection performed in Fossat and Schmider (2018) is an artefact of the methodology.