Here's a tidbit from Patrick Madrid's book Answer Me This! (Indiana: Our Sunday Visitor, 2003) p.176.
The Catholic Church did not add [the Apocryphal books] at the Council of Trent. Rather, it was the early Protestant reformer Ulrich Zwingli who most notably deleted the Deuterocanonical books from his edition of the Bible.
I wasn't aware Zwingli actually single-handily produced a translation of the Bible. I assume Mr. Madrid is referring to The Zürich Bible, which was a project Zwingli was involved with, though by no means the mastermind behind it (like Luther was his German Bible). Leo Jud is typically the man credited for the majority of the project. As far as I know, Zwingli wasn't responsible for any of the translation, though a preface is attributed to him with reservations.
Did the Zürich Bible delete the Apocrypha? No.
The first edition of the Swiss-German Bible was published in six volumes (Zurich, 1527-29), the fifth of which contains the Apocrypha. The title page of this volume states, "These are the books which are not reckoned as biblical by the ancients, nor are found among the Hebrews." A one-volume edition of the Zurich Bible, which appeared in 1530, contains the apocryphal books grouped together after the New Testament [source]
Roman Catholic apologist Gary Michuta says this about the Zürich Bible:
The Alsatian Zwinglite, Leo Jud, produced a translation of Scripture known as the Zurich Bible (1531). The Deuterocanon is included in an appendix titled "Apocryphi." Jud justifies his inclusion of the appendix so that those who read them and like them will not complain about their absence. He claims to have followed the Fathers in that they did not include the Deuterocanon among the Holy Scripture. However, Jud states,
... [Y]et they [the Deuterocanon] contain much which in no way contradicts the biblical writings, faith and love, and some things which are founded in God's word.
Completed in 1531, three years before the publication of Luther's bible, the Zurich Bible matches Luther's translation in contents and order. Another preface of the Zurich Bible, commonly ascribed to Zwingli, states that the Apocrypha is not highly esteemed, being less clear and accurate that the Protocanon, although the books contain much that is true and useful. Zwingli leaves it up to the reader to divide the good from the bad. Like Jud's preface, Zwingli states that the Apocrypha has been included in the Zurich Bible "so that no one may complain of lacking anything, and each may find what is to his taste.
In the 1543 edition of the Latin Zurich Bible, the title of the Apocryphi appendix was changed to "Church Books" (Ecclesiastici Libri). The preface states:
Church Books which the Church always held to be holy books, worthy for the pious to read. Yet they were not given equal authority with the canonical writings. Our forefathers wanted them to be read in the churches, but not drawn on to confirm the authority of faith (articles of faith). So they were called apocrypha, a word which is not in every respect appropriate or suitable for them. They had no validity among the Hebrews, but were brought to light again among the Greeks." [Gary Michuta, Why Catholic Bibles Are Bigger, p.257-258].