We propose Implicit Quote Extractor, an end-to-end unsupervised extractive neural summarization model for conversational texts. When we reply to posts, quotes are used to highlight important part of texts. We aim to extract quoted sentences as summaries. Most replies do not explicitly include quotes, so it is difficult to use quotes as supervision. However, even if it is not explicitly shown, replies always refer to certain parts of texts; we call them implicit quotes. Implicit Quote Extractor aims to extract implicit quotes as summaries. The training task of the model is to predict whether a reply candidate is a true reply to a post. For prediction, the model has to choose a few sentences from the post. To predict accurately, the model learns to extract sentences that replies frequently refer to. We evaluate our model on two email datasets and one social media dataset, and confirm that our model is useful for extractive summarization. We further discuss two topics; one is whether quote extraction is an important factor for summarization, and the other is whether our model can capture salient sentences that conventional methods cannot.