John Chrysostom

"Salute all them that have the rule over you, and all the saints. They of Italy salute you. Grace be with you all. Amen." "Salute them that have the rule over you, and all the saints." See how he honored them, since he wrote to them instead of to those (their rulers). "They of Italy salute you. Grace be with you all. Amen." Which was for them all in common. But how does "Grace" come to be "with" us? If we do not do despite to the benefit, if we do not become indolent in regard to the Gift. And what is "the grace"? …

Homily on Hebrews 34 ↗

Theophylact of Ohrid

See what honor he bestows upon them, if he even greets the teachers through them; for it would have been more fitting for him to write the epistle to the teachers and through them greet those under their charge. By this he very wisely ministers especially to the weak. I am so attached to you that not only do I myself greet you, but I inspire such affection for you in others as well, so that they too, despite such a great distance, love you, and therefore send their greetings.

Commentary on Hebrews ↗

Oecumenius

"Greet all your leaders." See how Paul honors them, for he addresses the leaders through them; for it was more fitting to command the leaders and to address the ones being led through them; but he wisely heals the weaker ones. "Those from Italy greet you." Therefore, I am so filled with you that not only do I greet you myself, but I also establish such a longing towards you in others, that even from such a distance they desire you, and for this reason, they greet you.

The Pseudo-Oecumenian Catena on Hebrews ↗

Thomas Aquinas

Then he gives the greeting: first, he asks them to greet the others, saying, Greet all your prelates, i.e., the apostles still living, and all the saints, namely, the other disciples. But he does not write to them, because his intention was to write only against the observances of the Law. Therefore, because this epistle is instructive, it was not his intention to instruct the apostles, who preceded him in the faith. Secondly, he salutes them on the part of the others, saying, The brethren from Italy send you greetings. …

Commentary on Hebrews ↗