Is it true that the Vilna Goan didnt let the Bal Hatanya in to speak with him and if so then why not

It is well known that the Bal HaTanya wanted to speak with the Vilna Goan to persuade him that Chassidus wasnt all that bad as the Gaon thought but the Gaon refused him entry.

I heard that the Gaon was told that by seeing the Bal HaTanya he would change his mind, to which the Vilna Gaon replied then he definitely doesn't want to speak to him? First of all, is the story true? And what could be pshat that he wouldnt discuss it?

The Previous Lubavitcher Rebbe writes that it says that

At that time, he secretly visited Shklov, Minsk, and Vilna. The Alter Rebbe spent six weeks in Vilna during that secret mission. He would wander from one beis hamedrash to another, disguised as a visiting traveler. Even on Shabbos, he would eat nothing but bread and water.

The gaon Reb Yehudah Leib, the Alter Rebbe's brother, told my great-grandfather the Tzemach Tzedek that while the Alter Rebbe was in Vilna, he discussed pilpul with all the great Torah scholars. But he refrained from engaging the Gaon Rav Eliyahu in discussion, for fear that he would be recognized. He did, however, submit several questions to him through two of his adherents. "I soon learned whom I was dealing with, and just how great his knowledge of the Torah was," said the Alter Rebbe to his brother.

So at least at one point in time, it was the Alter Rebbe who avoided the Gra.

Here are the fact of the story, as allegedly told by the Baal HaTanya [=Alter Rebbe] in his own words:

(Source: "Iggros Baal HaTanya U'bnei Doro", 56)

הנה מראשית כזאת הודענו והלכנו אל הגאון החסיד נ״י לביתו להתווכח עמו ולהסיר תלונותיו מעלינו, בהיותי שם עם הרב ההסיד המנוח מהור״ר מענדיל האראסנער זצלה"ה, וסגר הדלת בעדנו פעמיים. וכאשר דברו לו גדולי העיר, רבנו, הנה, זה הרב המפורסם שלהם יבא להתווכח עם כת״ה, וכאשר ינוצח בוודאי הנה בזה יהיה שלום על ישראל, דחה אותם בדיחויים. וכאשר החלו להפציר בו מאד חלף והלך לו ונסע מן העיר ושהה שם עד יום נסיעתנו מהעיר, כידוע לזקני עירם.

Why did the allegedly Gra refuse to speak to the Baal HaTanya?

The Baal HaTanya himself tried to figure out why (see ibid.). However in the absence of a reliable source from the Gra's camp, the Gra's true motives remain pure conjecture.