Home-ly courtesy is a catchy description of Julian's God—not homely in the sense of "plain or unattractive" but in the comfortable sense of "down-home". The phrase also describes a way of living that we should aspire to.
Julian writes, "The place that Jesus takes in our soul, He will never move it away forever, as I see it, for in us is His most familiar home and His eternal dwelling….And therefore the blessed Trinity rejoices without end in the creating of man's soul, for He saw from without beginning what would please Him without end". (Ch. 67)
It is hard for ordinary people really to feel that their souls are so dear to the Creator of the universe, a dear-ness so long-lasting, that their souls have been chosen as God's dwelling place. And to be astounded that God still keeps His residence there despite the many faults, irritations, mistakes they may commit.
"I love you for yourself." Those magical words between two human persons are always hard to take in as well. The reality of those words is proved by the willingness of each person to carry on loving despite obvious (or not so obvious) faults and irritations in the other. That patience and acceptance comes from the quality of mercy: "protecting, enduring, bringing life, and healing, and all is from the tenderness of love". (Ch. 48) But a mercy augmented by grace, that is, by treating each other with courtesy. "For while our Lord Himself is supreme friendliness, He is also as courtly as He is friendly, for He is true courtesy". (Ch. 77)
And, simply to make it straightforward, it is of course the “new” commandment our Lord gave us—the hardest one to fulfill as long as we rely on ourselves.