Why did Regan kiss the priest at the end?

I think in a way, she knew that someone helped her and that it was a man of the cloth.

She saw the collar which triggered a memory

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Important part of the movie. That, along with the part afterwards where that same priest advises the mother to keep the necklace of the saint, which belonged to Father Karras. I think both of these parts help cement the resolution that even though the priests died, they and God defeated the demon.