“reminder symbols.” These reminder symbols are the reminders that the Israelites were to write on their doors, obviously in a place where they could be seen, to remind them that Yahweh was to be their only God and they were to follow Him and obey His Law. To excuse her shameful activity and not be reminded of Yahweh, Israel moved these reminders from the doorpost to behind the doors and the posts. Removing God from their eyes and hearts, they practiced their idolatry and cultic sex “away from” God: “This people honors me with their lips, but their heart is far from me” (Matt. 15:8; cp. Isa. 29:13).
Some commentators and translations support the idea that these symbols are pagan symbols, but that does not seem to fit the context nearly as well as them being the reminder symbols that God commanded. The Israelites were openly practicing idolatry and cultic sex, so why would they put a symbol for it out of sight behind the door? Keil and Delitzsch write, and ably defend their conclusion: “The zikkaron, i.e., the declaration that Jehovah is the only God, which the Israelites were to write upon the posts of their houses, and upon the entrances (Deut. 6:9; 11:20) for a constant reminder, she had put behind the door and the post, that she might not be reminded, to her shame, of her unfaithfulness” (Commentary on the Old Testament).
“at their genitals.” The Hebrew text is literally at their “hand.” Here the word “hand” is an idiom and stands for the genitals. Just as in that ancient society, a man’s hand was his strength and power, so too his ability to have children, especially sons, was strength and power (cp. Ps. 127:4-5), and on that basis of that comparison, the genitals were spoken of idiomatically as the “hand.” The firstborn son of a man was “the beginning of his strength” (Deut. 21:17). Although this is the only use of this idiom in the Bible, Keil and Delitzsch (Old Testament Commentary) point out that “Arabic furnishes several analogies to this obscene use of the word,” and John Oswalt (The New International Commentary on the Old Testament: Ezekiel) notes that “hand” is used for penis in Egyptian and appears to be in Ugaritic as well.