And what was declared by Pope Damasus was in part rejected by Trent.
Once Luther removed the problematic Apocryphal books, it became necessary to render final, binding definition of the canon.
It wasn't just Luther who "removed" the problematic Apocryphal. The historical evidence given by the R.C. scholar Cardinal Catejan (Luther's adversary in other matters) along with other substantial historical evidence from sources such as the The Glossa Ordinaria indicates that the general practice of the Western church from the time of Jerome until the Reformation was to follow the distinctions of Jermone, Rufinus and Athanasius regarding the ecclesiastical and canonical books.
Cordially,
What part was rejected by Trent? Trent re-iterated the canon as declated by Damasus.
I politely differ:
http://www.newadvent.org/cathen/03267a.htm
In the Latin Church, all through the Middle Ages we find evidence of hesitation about the character of the deuterocanonicals. There is a current friendly to them, another one distinctly unfavourable to their authority and sacredness, while wavering between the two are a number of writers whose veneration for these books is tempered by some perplexity as to their exact standing, and among those we note St. Thomas Aquinas. Few are found to unequivocally acknowledge their canonicity. The prevailing attitude of Western medieval authors is substantially that of the Greek Fathers. The chief cause of this phenomenon in the West is to be sought in the influence, direct and indirect, of St. Jerome's depreciating Prologus. The compilatory "Glossa Ordinaria" was widely read and highly esteemed as a treasury of sacred learning during the Middle Ages; it embodied the prefaces in which the Doctor of Bethlehem had written in terms derogatory to the deuteros, and thus perpetuated and diffused his unfriendly opinion. And yet these doubts must be regarded as more or less academic. The countless manuscript copies of the Vulgate produced by these ages, with a slight, probably accidental, exception, uniformly embrace the complete Old Testament Ecclesiastical usage and Roman tradition held firmly to the canonical equality of all parts of the Old Testament There is no lack of evidence that during this long period the deuteros were read in the churches of Western Christendom.