Genesis 24:40 (from Sefaria - modified English by me):
וַיֹּ֖אמֶר אֵלָ֑י יְהוָ֞ה אֲשֶׁר־הִתְהַלַּ֣כְתִּי לְפָנָ֗יו יִשְׁלַ֨ח מַלְאָכ֤וֹ אִתָּךְ֙ וְהִצְלִ֣יחַ דַּרְכֶּ֔ךָ וְלָקַחְתָּ֤ אִשָּׁה֙ לִבְנִ֔י מִמִּשְׁפַּחְתִּ֖י וּמִבֵּ֥ית אָבִֽי׃
And he said unto me: The LORD, before whom I walk, will send His angel with you, and make your way successful; and you shall take a wife for my son from my family, and from my father’s house;
If you view Genesis 24:4:
כִּ֧י אֶל־אַרְצִ֛י וְאֶל־מוֹלַדְתִּ֖י תֵּלֵ֑ךְ וְלָקַחְתָּ֥ אִשָּׁ֖ה לִבְנִ֥י לְיִצְחָֽק׃
But you shall go to my country, and to my birthplace, and take a wife for my son, for Isaac
There is no explicit command from Avraham indicating that Eliezer should get a wife specifically from Avraham's family.
Is it possible that Eliezer "expanded" on his relating the story after the fact since, as it turns out, he was in Avraham's family's home?