Unctuously (adjective) – full of unction; especially : revealing or marked by a smug, ingratiating, and false earnestness or spirituality

https://www.merriam-webster.com/dictionary/unctuously

“”You must,” the Reverend Mr. Pleasant Green would say unctuously, “trust the Lord more fully, Helga.” (277 online version)

Understanding this word tells me how he said what he said towards Helga. He said it trying to sound earnest and righteous in a way so it seems and sounds right despite her view on God in the past.