Here's the passage from that paper that explains the 0.3% figure from the abstract:

From publication and citation data, Anderegg et al. (2010) selected 908 of 1,372 climate researchers, defined as scientists who had published at least twenty climate papers and had either signed petitions opposing or supporting the IPCC’s positions or had co-authored IPCC reports. Of these, 97–98 % endorsed the standard definition that ‘‘anthropogenic greenhouse gases have been responsible for ‘most’ of the ‘unequivocal’ warming of the Earth’s average global temperature over the second half of the twentieth century’’(p. 12107). The standard definition of the consensus in Anderegg et al. (2010) is less imprecise than that of Cook et al. (2013). Yet, like Cook et al. (2013), Anderegg et al.(2010) did not seek to determine how many researchers considered this global warming to be actually or potentially damaging enough to require a climate policy.

Such surveys are often cited as demonstrating a near-unanimous scientific consensus infavor of a climate policy, when they never ask any question about whether and to what extent the anthropogenic component in recent warming might be dangerous or about whether a ‘‘climate policy’’ should be adopted in attempted mitigation of future warming. Nevertheless, Cook et al. (2013), after a subjective review of only the abstracts of 11,944 papers on climate change which ‘‘matched the topics ‘global climate change’ or ‘global warming’’’ (p. 1), conclude that 97.1 % of those that expressed an opinion endorsed the hypothesis as defined in their introduction (i.e.,the standard definition). However, 66.4 % percent of the abstracts had expressed no position. Thus, 32.6 % of the entire sample, or 97.1 % of the 33.6 % who had expressed an opinion, were said to be in agreement with the standard definition. However, inspection of the authors’ own data file showed that they had themselves categorized only 64 abstracts, just 0.5 % of the sample, as endorsing the standard definition. Inspection shows only 41 of the 64 papers, or 0.3 % of the sample of 11,944 papers, actually endorsed that definition.

I had a little bit of trouble parsing that text alone, but the underlying data was easier to digest - here's the breakdown of analyzed papers by "level of endorsement of the climate consensus", from Table 1 of that same paper:

Endorsement level Abstracts % of All Abstracts
------------------------------------------------------------------- --------- ------------------
Explicit, quantified endorsement (standard definition of consensus) 64 0.54%
Actually endorsing the standard definition upon inspection 41 0.34%
Explicit, unquantified endorsement 922 7.72%
Implicit endorsement 2910 24.36%
No Position 7930 66.39%
Expression of uncertainty 40 0.33%
Implicit rejection 54 0.45%
Explicit, unquantified rejection 15 0.13%
Explicit, quantified rejection 9 0.08%
Total 11944 100.00%

The 0.3% from the abstract refers to the 0.34% of papers that provide "explicit, quantified" endorsement of the consensus that "anthropogenic greenhouse gases have been responsible for ‘most’ of the ‘unequivocal’ warming of the Earth’s average global temperature over the second half of the twentieth century". But the majority of abstracts neither endorsed nor rejected that consensus, while the vast majority (97.1%) of those expressing an opinion either explicitly or implicitly endorsed the consensus view.

This doesn't strike me as a particularly strong refutation to throwaway5752's claim.