The only mention of Hametz in the Haggadah (besides the Bedikat Hametz blessings and Aramaic legal nullification formula traditionally tacked on to the beginning of the Haggadah) is in the 4 Questions:
יהי רצון מלפניך א-דני א-להינו וא-להי אבותינו כשם שאני מבער חמץ מביתי ומרשותי
כך תבער את כל החיצונים, ואת רוח הטומאה תעביר מן הארץ,
ואת יצרנו הרע תעבירהו מאתנו,
ותתן לנו לב בשר לעבדך באמת,
וכל סטרא אחרא וכל הקליפות וכל הרשעה בעשן תכלה
ותעביר ממשלת זדון מן הארץ,
וכל המעיקים לשכינה תבערם ברוח בער וברוח משפט,
כשם שבערת את מצרים ואת אלהיהם בימים ההם בזמן הזה אמן סלה
For the nullification of the chametz say:
All leaven and anything leavened that is in my possession, whether I have seen it or not, whether I have observed it or not, whether I have removed it or not, shall be considered nullified and ownerless as the dust of the earth.
The ten pieces are to be burnt, and the following is said during the burning of the chametz:
May it be Your will, Lord, our G‑d and G‑d of our fathers, that just as I remove the chametz from my house and from my possession, so shall You remove all the extraneous forces.
Remove the spirit of impurity from the earth, remove our evil inclination from us, and grant us a heart of flesh to serve You in truth.
Make all the sitra achara, all the kelipot, and all wickedness be consumed in smoke, and remove the dominion of evil from the earth. Remove with a spirit of destruction and a spirit of judgment all that distress the Shechina, just as You destroyed Egypt and its idols in those days, at this time. Amen, Selah.
רבי לוי-יצחק מברדיטשוב ז״ל, משהיה רואה בערבי פסחים נשים עוסקות בניקוי וכשרת הבית והכלים, תוך גירוד, קירצוף, שטיפה ורחיצה, היה אומר כדרך שאומרים בשעת תקיעת-שופר בראש-השנה: ״יהי רצון שאלה המלאכים היוצאים מן קשר״ק (קירצוף, שטיפה, רחיצה, קירוד) יעלו לפני כסה כבודך וימליצו טוב בעדנו״...
והיינו, שכל ההכנות הללו יוצרות מלאכים מליצי-יושר לישראל...
הגדה של פסח, עם מעינה של תורה נעספו על ידי אלכסנדר זושה פרידמן, הוצת פאר תל-אביב 1957
Rabbi Levi Yitzchak of Berditchev, when he saw, on the eve of Passover, women engaged in cleaning and kashering the home and kitchen utensils, through scrubbing, washing, scraping and rinsing, would say as they say at the moment of blowing the shofar on Rosh Hassanah: May it be Your will that these angels that come out of "KiSRIK" (Scraping, Rinsing, washing and scrubbing) rise to the throne of Your abode and advocate good for us.... Which means to say, that all these preparations create angels who suplicate on behalf of Israel.
Passover Haggadah with Springs of Torah gathered by Alexander Zusha Freidman, Published by Paer Tel Aviv, 1957 (HEBREW)
Greco-Roman Concept of Leaven
“Leaven itself comes from corruption, and corrupts the dough with which it is mixed . . . and in general, fermentation seems to be a kind of putrefaction” (Plutarch, Quaest. Rom. 109). Plutarch records that the Roman high priest (Flamen Dialis) was forbidden even to touch leaven (ibid.). To be sure, all of the above-cited references stem from late antiquity (Christian, rabbinic, and Hellenistic sources), but they undoubtedly reflect an older and universal regard of leaven as the arch-symbol of fermentation:’ deterioration, and death and, hence, taboo on the altar of blessing and life. [pp 188-9 Leviticus 1-16: A New Translation with Introduction and Commentary Anchor Bible, Vol. 3, Jacob Milgrom]
Leaven in Philo
Leaven is forbidden because of the rising which it produces. Here again we have a symbol of the truth, that none as he approaches the altar should be uplifted or puffed up by arrogance; rather gazing on the greatness of God, let him gain a perception of the weakness which belongs to the creature, even though he may be superior to others in prosperity; and having been thus led to the reasonable conclusion, let him reduce the overweening exaltation of his pride by laying low that pestilent enemy, conceit. …. For naked you came into the world, worthy sir, and naked will you again depart, and the span of time between your birth and death is a loan to you from God. During this span what can be meet for you to do but to study fellow-feeling and goodwill and equity and humanity and what else belongs to virtue, and to cast away the inequitable, unrighteous and unforgiving viciousness which turns man, naturally the most civilized of creatures, into a wild and ferocious animal! (Philo,The Special Laws, Book I, 293-295 quoted in The Passover Anthology, Philip Goodman).
Leaven in the New Testament
Therefore let us keep the feast, not with old leaven, neither with the leaven of malice and wickedness; but with the unleavened [bread] of sincerity and truth. [Corinthians 5:8]
“the leaven of the Pharisees,” which is “hypocrisy” (Luke 12:1; d. Mark 8:15).
It could be that Leaven and the purging of Leaven had become, at least in the early days of Jewish - Christian relationships, a wedge issue.... especially given the reference to the "leaven of the Pharisees" aka followers of Rabbinic Judaism.
Jewish-Christian tensions in the Middle Ages
We return to the question of why the purging of physical leaven and the leaven of our hearts is seemingly absent from our Seder. Israel Jacob Yuval details the conflagratory nature of "leaven" in Jewish-Christian tensions in the Middle Ages. In his article Passover in the Middle Ages in Passover and Easter; Origin and History to Modern Times pp 141-2 writes:
But burning leaven evoked messianic images of redemption, as we see from the thirteenth-century halakhic authority and German pietist, Eliezer of Worms: “As reward for the burning of leaven, Israel will set Esau [Rome] on ﬁre.” Little imagination is needed to guess what Christians who observed the ceremony must have thought. On the eve of Passover, on the day which (as Jews reckoned it) Jesus was crucified, Jews removed all leaven from their home and burned it—while thinking of the destruction of Christianity and the coming of redemption. Some Jews themselves feared that interpretation....
The following event, however, reveals the danger that existed in that regard. In the year 1399, a disputation occurred between the convert from Judaism, Peter, and Rabbi Lipmann Mulhausen. The remarkable conclusion of the disputation— the execution of eighty Jews—evokes the impression that this was not a learned debate so much as it was an inquisitorial trial played out against the backdrop of the charge of host desecration [The "host" is the sacred bread used in the Eucharistic service of the Mass]. The central Christian argument was that Jews disdain Christianity and seek to destroy it: “Of all the dough that you knead, you burn a little as an affront to their God [i.e., the Christian God]. Also, on the eve of Passover, the time of the fast [Lent] you burn bread.” The accusations refer to two customs: burning challah (the ritual removal and burning of part of the dough as an equivalent to the dough offering from Temple times, before baking bread) and burning leaven. The apostate from Judaism apparently saw in both a Jewish effort to disparage the host.
Spiritual Spring Cleaning - Persia/India - Zoroastrian
House cleaning, or shaking the house (Persian: خانه تکانی, romanized: xāne tekāni) is commonly done before the arrival of Nowruz. People start preparing for Nowruz with a major spring cleaning of their homes.
People prepare to welcome the new year days before by spring cleaning and arranging the “haft
seen”, a table with seven items that name start with the letter “s”. Al-bīrūnī said: haft-sin came from jamshid since he destroyed the evil that made persian lands weak.
At this time of year in Iran, you’re likely to see countless persian rugs hanging outside, where their owners can beat the dust out of them. For Iranians, nowruz is a celebration of renewal and change.
Spiritual Spring Cleaning - Orthodox Christianity
Similarly Lent comes from the word length.. as in the longer days of spring. Instead of Ash Wednesday, the Eastern Church celebrates Clean Monday, otherwise known as Ash Monday. According to Wikipidia:
The common term for this day, “Clean Monday”, refers to the leaving behind of sinful attitudes and non-fasting foods. It is sometimes called “Ash Monday,” by analogy with Ash Wednesday (the day when the Western Churches begin Lent). …. Liturgically, Clean Monday—and thus Lent itself—begins on the preceding (Sunday) night, at a special service called Forgiveness Vespers, which culminates with the Ceremony of Mutual Forgiveness, at which all present will bow down before one another and ask forgiveness. In this way, the faithful begin Lent with a clean conscience, with forgiveness, and with renewed Christian love. The entire first week of Great Lent is often referred to as “Clean Week,” and it is customary to go to Confession during this week, and to clean the house thoroughly.
Psalms read Read on Monday and Thursday during Lent include: