I've never heard of Wolsey's dog biting the Pope and, as far as I know, Wolsey didn't go to the Vatican. However, martyrologist John Foxe, author of Actes and Monuments (Foxe's Book of Martyrs) tells a story of Cranmer, Stokesley, the Earl of Wiltshire (Thomas Boleyn) and other learned men being sent to see the Pope to plead the case for the annulment and Wiltshire's spaniel biting the Pope's big toe when he put his foot out to be kissed. This story can be read in the chapter "The Life and Story of Archbishop Cranmer":-
"And when the time came that they should come before the bishop of Rome to declare the cause of their ambassage, the bishop, sitting on high in his cloth of estate and in his rich apparel, with his sandals 'on his feet, offering as it were his foot to be kissed of the ambassadors ; the earl of Wiltshire, disdaining thereat, stood still, and made no countenance thereunto, so that all the rest kept themselves from that idolatry. Howbeit, one thing is not here to be omitted, as a prognosticate of our separation from the see of Rome, which then chanced by a spaniel of the earl of Wiltshire, For he, having there a great spaniel which came out of England with him, stood directly between the earl and the bishop of Rome, when the said bishop had advanced forth his foot to be kissed. Now whether the spaniel perceived the bishop's foot of another nature than it ought to be, and so taking it to be some kind of repast — or whether it was the pope's will of God to show some token by a dog unto the bishop of his inordinate pride, that his feet were more meet to be bitten of dogs, than kissed of christian men — the spaniel (I say), when the bishop extended his foot to be kissed, no man regarding the same, straight-way (as though he had been of purpose appointed thereunto) went directly to the pope's feet, and not only kissed the same unmannerly Avith his mouth, but, as some plainly reported and affirmed, took fast with his mouth the great toe of the pope, so that in haste he pulled in his glorious feet from the spaniel : whereat our men smiling in their sleeves, what they thought, God knoweth."
Actes and Monuments, Vol VIII p9, see http://www.archive.org/stream/actsmonumentsofj08foxe#page/8/mode/2up