To be clear, they didn’t didn’t edit out GC sites that “caused problem with a monophyletic hypothesis”, they edited out GC sites that were contributing to the unresolved nature of classifications with Chlorophyta. The phylogeny of the classes within Chlorophyta (as well as the monophyly of some of these classes) was thus far unresolved, giving conflicting results and weak support in different studies. Fang et al set out to resolve these conflicts - to find the real phylogeny, regardless of what it was. There’s nothing to suggest that the authors were cherry-picking sites to remove in order to support a particular phylogeny, as you seem to be suggesting.
Their reasoning holds up - if GC heterogenous sites are known to be rapidly-evolving and lacking any useful phylogenetic signal, it stands to reason that they be removed, reducing the noise in the rest of the analysis.
Are you suggesting that these phylogenetically “uninformative” sites are actually some kind of signature of seperate ancestry? Can you elaborate on that?