Looking at the temperature, total solar irradiance graphs in your links, the TSI levels off after 1970 while the temperature continues to increase. Hence the argument that TSI variation is not correlated with temperature variation.

Now if you plot atmospheric carbon dioxide vs temperature, you will note that between 1940 and 1970, CO2 increases while temperature decreases. Thus the same argument says that CO2 variation is not correlated with temperature variation.

TomT