“When he came down from the mountain, great crowds followed him. And behold, a leper came to him and knelt before him, saying, ‘Lord, if you will, you can make me clean.’ And Jesus stretched out his hand and touched him, saying, ‘I will; be clean.’ And immediately his leprosy was cleansed” (Matthew 8:1-3).
Second, note the first person Jesus, who had just made an invitation into his kingdom and explained what kind of righteousness was, not only required, but was to flow from living in the kingdom, encounters–the first–was a leper. This, of all people in the land, is one of the target groups of the Beatitudes, a much marginalized social class, and very unclean.
Third, note that Jesus touched the leper before he healed him—significant, because you don’t touch lepers and if you do, you share in their uncleanness (get it?).
Then, finally note, the kingdom is realized when “immediately” the leper was made clean. You must remember that pure of heart in 5:8 is actually [ socially, religiously] "clean of heart"). So there is a definite narrative pun (connection) here for the reader to catch.
This narrative was no interruption, but was the sermon's application.
Now go and do likewise.