Catholics are not bound to hold that the verses were written by St. Mark. But they are canonical Scripture, for the Council of Trent (Sess. IV), in defining that all the parts of the Sacred Books are to be received as sacred and canonical, had especially in view the disputed parts of the Gospels, of which this conclusion of Mark is one (cf. Theiner, “Acta gen. Conc. Trid.”, I, 71 sq.). Hence, whoever wrote the verses, they are inspired, and must be received as such by every Catholic.
That being said, this should be added…
The external evidence in favour of the long, or ordinary, conclusion is exceedingly strong. The passage stands in all the great unicals except B and Aleph–in A, C, (D), E, F, G, H, K, M, (N), S, U, V, X, Gamma, Delta, (Pi, Sigma), Omega, Beth–in all the cursives, in all the Latin manuscripts (O.L. and Vulg.) except k, in all the Syriac versions except the Sinaitic (in the Pesh., Curet., Harcl., Palest.), in the Coptic, Gothic, and most manuscripts of the Armenian. It is cited or alluded to, in the fourth century, by Aphraates, the Syriac Table of Canons, Macarius Magnes, Didymus, the Syriac Acts of the Apostles, Leontius, Pseudo-Ephraem, Cyril of Jerusalem, Epiphanius, Ambrose, Augustine, and Chrysostom; in the third century, by Hippolytus, Vincentius, the “Acts of Pilate”, the “Apostolic Constitutions”, and probably by Celsus; in the second, by Irenæus most explicitly as the end of Mark’s Gospel (“In fine autem evangelii ait Marcus et quidem dominus Jesus”, etc.–Mark xvi, 19), by Tatian in the “Diatessaron”, and most probably by Justin (“Apol. I”, 45) and Hermas (Pastor, IX, xxv, 2). Moreover, in the fourth century certainly, and probably in the third, the passage was used in the Liturgy of the Greek Church, sufficient evidence that no doubt whatever was entertained as to its genuineness. Thus, if the authenticity of the passage were to be judged by external evidence alone, there could hardly be any doubt about it.
So if the longer ending was quoted as early as the second century by Irenaeus, Tatian in the Diatessaron, Justin Martyr and the Shepherd of Hermas, that goes a long way to establish both its authenticity and legitimacy as the intended ending.