1 Monty: {walking down a passage in the Vatican} So we've done the hard part? Getting past the guards?
2 Ginny: You're forgetting two things...
3 Minnesota Jones: The Pope's rottweilers! {two vicious looking dogs block the passage ahead}
4 Monty: I thought that was a joke.
4 Ginny: I never joke about ecclesiastical sentinel beasts.

I didn't know until I did some research for this annotation, but apparently there are strict rules against animals being in the Vatican. So strict that Pope Benedict XVI, who as Cardinal Ratzinger prior to his election as Pope owned two cats, was not allowed to bring them into the Vatican to live with him.

This rule appears to have been instituted in the 20th century, as Pope Leo XII had a pet dog. I wasn't able to turn up any further information though, particularly on why this prohibition on pets in the Vatican exists. Maybe somewhere along the line someone got mauled by the Pope's rottweilers.

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2017-06-14 Rerun commentary: Apparently quite a few people have posed the question on the Internet of whether the Pope is allowed to have pets. The answer seems to be that he can have pets, but is not allowed to bring them into the Vatican. Pope Benedict XVI kept his cats in a private apartment outside the Vatican with a caretaker, and went to visit them every now and then.

More information here, including some speculation as to why this rule exists.