The Jamieson, Fausset, and Brown Commentary on this verse says, 'And have returned to provoke me to anger: and, lo, they put the branch to their nose - proverbial, because 'they turn up the nose in scorn,' expressing their insolent security. (Septuagint) Not content with outraging 'with their violence' the second table of the law--namely, that of duty toward one's neighbour - 'they have returned' (i.e., they turn back afresh) to provoke me by violations of the first table (Calvin). Rather, they held up a branch or bundle of tamarisk branches (called barsom) to their nose at daybreak, while singing hymns to the rising sun (Strabo, i. 15, p. 733). Sacred trees were frequent symbols in idol-- worship. Calvin translates, 'to their own ruin'--literally, 'to their nose' -- i.e., with the effect of rousing my anger (of which the Hebrew is 'nose') to their ruin.'
Matthew Henry's Commentary says, 'And, lo, they put the branch to their nose'—a proverbial expression denoting perhaps their scoffing at God and having him in derision; they snuffed at his service, as men do when they put a branch to their nose. Or it was some custom used by idolaters in honour of the idols they served. We read of garlands used in their idolatrous worships (Acts 14:13), out of which every zealot took a branch which they smelled to as a nosegay. Dr. Lightfoot (Hor. Heb. in John 15.6) gives another sense of this place: They put the branch to their wrath, or to his wrath, as the Masorites read it; that is, they are still bringing more fuel (such as the withered branches of the vine) to the fire of divine wrath, which they have already kindled, as if that wrath did not burn hot enough already. Or putting the branch to the nose may signify the giving of a very great affront and provocation either to God or man; they are an abusive generation of men.'