Repeating as a positive listening technique can be in effort to show the person that you are actually listening to them, not just thinking about what you're going to say or what you think. It works to make the other person feel heard. And it can work to clarify whether you understood them correctly. It's a way of asking that... "The sky is yellow." "The sky is yellow?" It may be of a more indirect style than you use, but it's still the same question.
Lark is asking about people repeating your own stories back to you, as if they were their own. Like:
He told Sam that he went fishing yesterday and caught a 100lb bass, and then when he stopped for gas on the way home, he bought a lotto ticket and won $100,000.
Tomorrow, when he asks how Sam is, Sam tells him he went fishing yesterday and caught a 100lb cod, and then on the way home, he bought a lotto ticket and won $95,000.
I would assume sarcasm, gas lighting, obnoxiousness, or not being all there mentally...