What's the term for a phrase someone uses repeatedly in conversation?

Solution 1:

I think 'phatic' is the word you're after - Of, designating, or relating to speech, utterances, etc., that serve to establish or maintain social relationships rather than to impart information, communicate ideas, etc.; esp. in phatic communion n. speech communication of this kind; (also) trivial or purely formal verbal contact.(OED)

Solution 2:

Palilalia, a complex tic, is a speech disorder characterized by the involuntary repetition of syllables, words, or phrases. Your case histories, however, display milder symptoms and sound more like habit tics.

• palilalia - a speech disorder in which a word or phrase is rapidly repeated.
• habit tic - A quirk or habit of behavior or language: common phrases that have become verbal tics.

Solution 3:

Mannerism is the word. A group of verbal or other unconscious habitual behaviors peculiar to an individual.