What is this scene parodying?
Thanks to @Krazer.

The characters in the scene seem to be Ikkyuu and Shin'emon from Ikkyū-san. 

The low-effort scribbles are signifying that they are characters from another series and want to avoid copyright issues, like how many MacDonalds in anime are called WacDonalds or similar.

I think it's not parodying a particular scene but instead just making fun of Shin'emon's cleft chin: