“to my nose.” Here in Ezekiel 8:17, the ancient scribes deliberately changed “my nose” to “their nose” to avoid offensive theology, and because that change is reflected in the standard Hebrew text, many English versions read “their nose” instead of “my nose.” The ancient scribes emended (changed) the text occasionally to, in their minds, preserve the sanctity of God.
The custom of putting a twig to the nose has been lost in antiquity, and scholars are not sure of its significance. A possible parallel might be a base-relief of a Syrian king holding a flower to his nose as he worshipped the stars (ANEP 281). If that is the case, it may be that God is telling Ezekiel that the worship of idols in the Temple was so bold and arrogant that it was as if the people of Judah were putting a branch to His nose so that He could worship their idols too.
It seems that the meaning of the custom was lost by 250 BC, because the Septuagint does not translate the phrase but translates a possible meaning: “and behold, they are like those who mock” (the LXX using muktērizō, “to turn up the nose at; to mock” to make the point).
About the change to the Hebrew text, E. W. Bullinger writes: “The Massorah, i.e., the small writing in the margins of the standard Hebrew codices…consists of a concordance of words and phrases, etc., safeguarding the Sacred Text. A note in the Massorah against several passages in the of the Hebrew Bible states: ‘This is one of the Eighteen Emendations of the Sopherim [Scribes]’, or words to that effect. Complete lists of these emendations are found in the Massorah of most of the model or standard codices of the Hebrew Bible, and these are not always identical; so that the number exceeds eighteen…” (Appendix 33, The Companion Bible).