The Gideons characteristically distribute the New Testament, along with the Books of Psalms and Proverbs from the Old Testament, in their school distributions. There is no "Deuteros" issue here. All Christian denominations agree on the content of the New Testament. Modern Catholic Bible translations, such as the New American Bible, use the same Greek text, called the Critical Text, as is used for modern Protestant translations, such as the New International Version and the New American Standard Bible.
Catholics, and for that matter, all religious believers, have a dog in this hunt. Any authority that can stop an evangelical men's ministry from distributing Bibles and tract literature can do the same to another group.