Theophylact of Ohrid

Elizabeth, being chaste, was ashamed and, having conceived in old age, "hid herself five months," until Mary also conceived. When she (Mary) also conceived, and the baby "leaped in her womb" (Elizabeth's), she no longer hid herself and even carried herself boldly, as the mother of such a son who even before his birth was honored with the dignity of a prophet.

Commentary on Luke ↗

Ambrose of Milan

And though she might blush at the time of her child-bearing, on the other hand she rejoiced that she was free from reproach, saying, Thus hath the Lord dealt with me. For it is a shame among women not to receive that reward of marriage, which is the only cause of their being married.

Catena Aurea by Aquinas ↗

Bede

And she hid herself for five months, saying, "Thus has the Lord dealt with me in the days when He looked on me, to take away my reproach among people." How much care the saints take to admit nothing shameful that should make them blush is shown by Elisabeth, who is even embarrassed by the gifts she desired to receive. And although she rejoices in the removal of the reproach of sterility, she is modest regarding the birth in her advanced age. …

On the Gospel of Luke ↗

Bonaventure

Fourthly, a joyful exultation is touched upon in recognition of the benefit, at: Saying, Because the Lord has done thus for me. Similarly Genesis 21: "The Lord has made laughter for me: whoever hears of it will laugh with me." — In the days in which he looked upon me to take away my reproach among men, the reproach, namely, of barrenness: Genesis 30: "Rachel conceived and bore a son, saying: God has taken away my reproach." This was a reproach among men, on account of that passage in Deuteronomy 7: "There shall not be one barren …

Commentary on Luke, Chapter 1 ↗