The "d" on "Used To"

This question came up on FB. When the letter t and the letter d are inside a word, they sound the same: ladder/latter, shudder/shutter, conceited/conceded. When the d ends one word and t starts the next word, they elide into one sound: ...talked to her... ...listened to the recording... In the combination with "used to" and "supposed to," this causes a problem. Be sure to add the "d" to the end of the verb in these combinations. However, when the helping verb "did" comes into the picture, there is no "d" on "use." ...He used to go with us. ...Did he use to go with us? Happy punctuating! Margie