That would be the past perfect tense, a different tense with a different meaning that is only used in the context of another past event you're talking about. The original quote is simple past tense and is correct.
You could also use the present perfect, "she has said goodbye too many times before", which sounds slightly better to me, but is again a different tense and implies the goodbye-saying is an ongoing phenomenon. If it's all in the past, this tense would be wrong.
You could also use the present perfect, "she has said goodbye too many times before", which sounds slightly better to me, but is again a different tense and implies the goodbye-saying is an ongoing phenomenon. If it's all in the past, this tense would be wrong.