Genesis 24:24 - Ellicott's Commentary On The Whole Bible

Bethuel the son of Milcah, which she bare unto Nahor. — Rebekah mentions her father’s mother to show that she was descended from a highborn wife; but the servant would welcome it as proving that not only on the father’s side, but also on the mother’s, she was Isaac’s cousin, Milcah being the daughter of Haran, Abraham’s brother. And when thus he knew that she fulfilled all the conditions, he gave her the jewels which he was holding in his hand, and bowed the head, and gave thanks.