Whose conversation does Percy overhear in Percy Jackson and The Lightning Thief? What are they discussing?

In Chapter Two, Percy overhears a conversation between Mr. Brunner and Grover. From all indications, they appear to be discussing Percy and his fate.

As the chapter begins, we discover that Percy's grades have slipped at Yancy Academy. When he hears that he will not be allowed back to school the next year, Percy experiences both positive and negative emotions. While he looks forward to seeing his mother again, he knows that he will miss Grover and Mr Brunner's Latin class. Above all else, he realizes that he will miss being around a teacher who believes in his ability to excel; that teacher would be Mr. Brunner.

Despite his misgivings, our young protagonist decides that he will make a last-ditch effort to prepare for his Latin final, both because of his teacher's faith in him and his teacher's admonishment that Latin would be a 'life-and-death' necessity for Percy. As he approaches Mr. Brunner's office, however, he realizes that his Latin master is having a private conversation with Grover.

Even though he feels a bit guilty, Percy can't help eavesdropping. In the conversation, he hears that Grover is worried about him being alone during the summer. Apparently, in both Grover and Mr. Brunner's eyes, the discovery of a 'Kindly One' at school is a worrisome development. However, Mr. Brunner advises that Percy should not be rushed into knowledge and that he should be given a chance to mature at his own pace.

Upon hearing this, Grover argues that time is not on their side and that they have the summer solstice deadline to meet. Mr Brunner's definitive answer is that the matter will have to be resolved without Percy's participation. Grover, still hesitant, voices his concern that Percy now knows who Mrs. Dodd is. However, at this point, Percy really does not know that Mrs. Dodd is actually one of the Furies (also called Kindly Ones) who serves Hades, the god of the Underworld. All he knows is that he fought Mrs. Dodd to the death after she revealed herself to him in her monster incarnation. Yet, curiously, no one seems to remember the existence of any teacher named Mrs. Dodd at the school.

Meanwhile, when Grover worries that he will fail at his efforts to protect Percy, Mr. Brunner encourages him by saying that they will only have to keep Percy alive until the following autumn. This statement disconcerts Percy so much that he unwittingly drops his mythology textbook in the hallway. The loud sound alerts Mr Brunner and Grover, and they become suspicious. However, Percy quickly manages to evade discovery by hiding in a nearby room. Eventually, Percy manages to make it back to his room after Grover leaves Mr. Brunner's office.