Two items, the silly one first and then the serious one.
First, did Pope Francis summon Kim Davis in order to thank and encourage her stand as a conscientious objector?
She was invited, along with many others, to a brief meeting with Francis, a routine activity in the Pope’s travels. She was invited, not by Francis, but by the Rev. Carlo Maria Vigano, a church bureaucrat who has been a fierce opponent of any same-sex activity beyond football.
Second, does she even qualify as a conscientious objector?
Again, the answer is no.
If you are a conscientious objector you refuse to obey an order, do so knowing the consequences and willing to accept those consequences. It is much like — may be considered a version of — civil disobedience. The point there is the same. You do not make a point by breaking the law. You make a point by accepting the consequences of that law-breaking.
Davis served a few days in jail then returned to her position and tried again to break the civil law for which she was jailed. That makes her, not a conscientious objector, but a serial miscreant.