Someone else must have made the following suggestion about the English expression "roof of the mouth," but I've never seen or heard it mentioned elsewhere. I wonder if the phrase might be derived from that part of the Mass in which we say "Domine, non sum dignus, ut intres sub tectum meum: sed tantum dic verbo et sanabitur anima mea" ("Lord, I am not worthy that thou shouldest come under my roof: but speak the word only, and my soul shall be healed"), just before receiving the body and blood of Christ under the appearance of bread and wine. In the jejune ICEL translation we hear at Sunday Mass nowadays, this becomes, "Lord, I am not worthy to receive you, but only say the word and I shall be healed."
This is a slight modification of the Vulgate Bible verse (Matthew 8:8) spoken by the centurion to Jesus: "Domine non sum dignus ut intres sub tectum meum sed tantum dic verbo et sanabitur puer meus" ("Lord, I am not worthy that thou shouldest come under my roof: but speak the word only, and my servant shall be healed"). The Latin word for roof is "tectum." In the centurion's case it was a literal roof; in the case of our mouths, it's a metaphorical roof.