Share 'Can snippets of dialogue be used well in one or two sentences of backstory?'

Or is it not good in your opinion? I'm revising now--and it's very easy for me to just cut it out--but I'm wondering about it. Perhaps it gives a more insightful view of the character recalling a tiny bit of conversation. There is over all, almost no backstory apart from a sentence or two sparsely placed. Yes, it has to relate to the story and to move the plot along--but can it also be enriching?…