How Is Mary’s Title Ark of the Covenant Connected to “Raiders of the Lost Ark?”

Not really, though it is related to the movie in a certain way in that in the litany (traditionally said after reciting the rosary) the Blessed Mother is compared to the Ark of the Covenant, which was being sought by Indiana Jones.

In the Old Testament (Ex 25:10ff) the Ark was a gold-covered box which bore three things: the written word of God on the stone tablets containing the Ten Commandments; the budded rod of Aaron, signifying his role as high priest; and a pot of manna, the mysterious “bread from heaven” which God gave to the Jews in the wilderness.

Mary is considered a symbol of the Ark because she, like the Ark, bore within her the Word of God (Jn 1:14), the true Bread from Heaven (Jn 6:33-35), and the High Priest of the New Testament (Heb 2:17).