Galileo was never jailed.
He was put under house arrest after staying with the Tuscan ambassador, and then at the residence of the archbishop of Siena for a few months.
The Pope you’re thinking of is Urban VIII.
And from what I’ve learned of the whole Galileo vs The Church deal,
if he’d not been so obnoxious about his theories and presented them in a more humble manner, there would have been no problem.
As it was, he was directly challenging the authority of the Catholic Church, not just presenting his new model.
Following the 1616 decree suspending for revision Copernicus' De Revolutionibus and an injunction by Cardinal Roberto Bellarmino not to hold or defend the Copernican doctrine, Galileo turned to the problem of the tides, hoping in doing to to provide a proof of the motion of the Earth. Galileo's pro-Copernican campaign culminated with the publication of his 1632 Dialogue concerning the two chief world systems. The Roman ecclesiastic authorities considered the book to violate the 1616 decree. In September 1632 Galileo was summoned to Rome by the Inquisition and was put on trial.
On June 22 1633 Galileo was forced to kneel in front of the Roman Inquisition and recant his beliefs in the Copernican doctrine and the motion of the Earth. He was then sentenced to life imprisonment, which was almost immediately commuted to perpetual house arrest without visitors, ostensibly for having disobeyed a 1616 injunction by Cardinal Bellarmine "...not to defend or teach the Copernican doctrine...". Galileo's Dialogue was put on the Index of Prohibited Books, as well as Copernicus' De Revolutionibus and the books of Kepler dealing with planetary theory.
Galileo's sentence was upheld rather rigidly despites numerous appeals to the Inquisition and the Pope by Galileo himself, as well as numerous prominent scientists and statesmen in Italy and Europe. After Galileo became blind in 1637, the enforcement of his sentence was relaxed somewhat, and he was allowed to receive visitors for extended periods of time. In 1638 he completed yet another landmark work, Discourses on Two New Sciences provided the foundations for the modern science of mechanics. The manuscript was smuggled out of Italy and the book published in Holland.
Galileo died on the evening of January 8, 1642. The Roman ecclesiastic authorities vetoed the public funeral and honor planned by the Florentine state. His books, together with those of Copernicus and Kepler, were removed from the Index in 1835, and only in 1992 did the Roman catholic Church formally admitted to having erred in dealing with Galileo.