John Chrysostom

"And when they perceived the grace that was given unto me, James and Cephas and John, they who were reputed to be pillars, gave to me and Barnabas the right hands of fellowship." He says not when they "heard," but when they "perceived," that is, were assured by the facts themselves, "they gave to me and Barnabas the right hands of fellowship." Observe how he gradually proves that his doctrine was ratified both by Christ and by the Apostles. …

Homily on Galatians 2 ↗

Theophylact of Ohrid

And again he mentions the three with praise. For "those reputed to be pillars," that is, the great ones whom everyone everywhere names and glorifies — they bear witness concerning me that my preaching is pleasing to Christ. Therefore they also "gave the right hand of fellowship," that is, they agreed, acknowledged us as partners, and showed that they were satisfied with my preaching, as in no way differing from their own word.

Commentary on Galatians ↗

Oecumenius

"And recognizing the grace." He presents as witnesses to Peter those about whom the grace was given to him. "who were thought to be pillars." They are, Paul says, pillars of the faith, esteemed by all. "They gave the right hand." Because the doctrines are common, and because they made us sharers with themselves in the declaration. For this reason they also gave the right hand, indicating that they approve of our preaching, he says, because it is the same as theirs. …

Commentary on Galatians ↗

Thomas Aquinas

But because one's appointment and authority to preach are not enough, unless he carries it out through good understanding and discreet eloquence and commends it by a good life, he adds how he used his authority or the effect of his office, saying, "And, when they had known the grace of God that was given to me, James and Cephas and John... …

Commentary on Galatians ↗