"Among the recipients of the funds are several charitable groups that are supposedly neutral on climate change, including the American Enterprise Institute (the top recipient of the funds) and the Heritage Foundation. "
This statement implies that the study identified funds designated for the purpose of CCCM, which organizations like AEI and Heritage accepted counter to their stated goals, but that is not what the study is saying.
The study started by looking at a list of 118 organizations and they examined reported income for those organizations. AEI and Heritage were included because the study authors decided to do so, and I have not seen the authors provide the coding sheets for individual organizations that would allow us to investigate why they were determined to be "CCCM" organizations.
In addition it appears that the majority of the organizations are coded as purpose level 2, which means that they do many different things. the 1B dollar figure is the total income for all organizations, so it would be wrong to presume that all of that went to CCCM activites.