The BBC Trust's editorial standards committee (ESC) apologised earlier this week over comments made by Boyle two years ago, comparing Palestine to a cake being "punched to pieces by a very angry Jew".
In his letter, the former Mock The Week star said he had been moved to tears after watching a documentary about life in Palestine and had promised himself he would do something.
He said that the BBC wished "to deliver the flavour of political comedy with none of the content", and also slammed the BBC's decision not to air a charity appeal for aid to Gaza last year. He said: "It's tragic for such a great institution, but it is now cravenly afraid of giving offence and vulnerable to any kind of well-drilled lobbying."
Boyle made the remarks on Radio 4 show Political Animal.
He said: "I've been studying Israeli Army martial arts. I now know 16 ways to kick a Palestinian woman in the back."