I teach this unit; at least, I imagine I do, as there's a version of it in a popular textbook.
Our version has been somewhat tweaked - which is something English Departments tend to do! - to address the needs of APP.
The assessed piece of work is a rather structured essay entitled 'How is humour used in the episode Homer Badman?'.
The specific assessment criteria require students to discuss the different types of comedy used & evaluate their effectiveness, & also to relate the text to social/cultural context (the portrayal of celebrities in the media, American v. British attitudes to scandal, & specifically hypocritical responses & how the media can manipulate them).
It's a good unit of work. Students are learning about multiple layers of meaning in a text, which is absolutely essential for GCSE. In fact, our ongoing misgiving as a Dept. has been in finding ways for weaker students to access the task.
It's currently (our version that is) having a major overhaul by one of my colleagues, because the key episode requires too much 'back history' on the Clinton/Lewinsky scandal: it's all a little bit dated!
But the complainant, I suspect, needs to take a proper look at the programme of study before getting out of his pram to start a petition, ffs.