The omission of alleluia during Lent goes back at least to the fifth century in the western church.
The association of alleluia with Easter led to the custom of intentionally omitting it from the worship service during the season of Lent, a kind of verbal fast which has the effect of creating a sense of anticipation and even greater joy when the familiar word of praise returns.
We do not use it at church. We do not use it at home. We let itrest, as it were, during Lent, so that when it reappears on Easter, we may hear it anew. In fact, once it returns on Easter, we give it no rest at all, repeating it again and again, in celebration of the Resurrection of Jesus.
The custom of actually bidding it farewell developed in the Middle Ages in Babylon. Many churches embrace the practice of physically “hiding” the alleluia. This ritual practice is especially delightful and meaningful for children.
Our Sunday School students have decorated an “Alleluia” scroll and hid it on Sunday, January 31, in preparation for Lent. The scroll will come out of hiding on Easter Sunday, March 27! (from the Episcopal Diocese of Texas: http://www.epicenter.org/formation/why-do-we-bury-the-alleluia/