Your question is excellent. The words of Rashi at the end of the Amud are difficult to understand. Rashi writes that according to Rebbi Yehudah, "this Tevilah was established in order to help a person remember if he became Tamei at an earlier time so that he will then refrain from entering the Azarah." Rashi then adds "And he will not do the Avodah today."

Why does Rashi mention Avodah? Even if he is not going to do any Avodah, it is Asur (with punishment of Kares) for a Tevul Yom to enter the Azarah (as Rashi himself mentions there)! This Rashi is very difficult to understand (indeed, RABEINU ELYAKIM gives the same explanation as Rashi but he omits the last words "v'Lo Ya'avod ha'Yom").

Our colleagues here in the Beis Medrash suggested that perhaps Rashi means as follows. When Rashi in the Mishnah writes that the word, "la'Avodah" is Lav Davka, this is problematic, for why, then, did the Mishnah mention it? (The Gevuras Ari deals with this question at length and gives a forced answer.) The SI'ACH YITZCHAK answers that the Mishnah is giving the reason for the requirement of Tevilah -- the reason it is forbidden to enter the Azarah without Tevilah even when one has no intention to perform an Avodah is because he might not only enter but end up doi actually performing an Avodah without remembering that he was Tamei. Therefore, the Chachamim prohibited entering the Azarah without Tevilah, even when one has no intention to do an Avodah.

However, this answer is difficult to understand, because it itself needs a reason -- why did the Chachamim not make a Gezeirah to prohibit the very entrance into the Azarah while one is Tamei? Why is the Gezeirah merely that one might enter and then do an Avodah while Tamei?

Rav Mordechai Rabin answered that the concern that one will enter the Azarah while Tamei is merely a concern for the person's own good, in order that he not be Chayav Kares or Chatas. Since his act of entry into the Azarah while Tamei would be inadvertent and unintended, that is not enough reason to enact a requirement for Tevilah. However, if he enters and he does Avodah while Tamei, this not only affects him, but it invalidates the Avodah and makes the Korban Pasul, and we will not find out about it until he remembers that he had become Tamei! Therefore, for the sake of the public for whom the Avodah is done, the Chachamim decreed that one must do Tevilah before entering the Azarah out of concern that perhaps he might do an Avodah.

According to this, we can now suggest that Rashi's intention here is that the Chachamim enacted this Tevilah in order for the person to remember that he is Tamei and thus refrain from entering the Azarah. But the real accomplishment of the enactment, Rashi adds, is that the public is protected as well, for that person will not do an Avodah and invalidate the Korbanos. This is the real reason why the Chachamim prohibited every person (even a Zar, as we see from the Sugya which requires a Metzora to do Tevilah for the Haza'ah on his thumbs) from even entering the Azarah without Tevilah.

-Mordecai