Mary stood before me, draped with my blanket like a nun and holding a napkin that had written on (it), You don't want to play with me anymore?
Should I write written on or written on it? I'm confused because I see both occurrences on Google.
When I follow the occurrences link in your question, I see three quotes, and all of them contain it.
The word order in your sentence is unusual, and maybe that's what is confusing you. Here is the sentence with a more conventional word order, and the actual text replaced by "something". When it is written like this, it should be clear that it is necessary.
Mary stood before me, draped in my blanket like a nun and holding a napkin that had something written on it.
The word order in your sentence is also valid when writing in a literary style:
Mary stood before me, draped in my blanket like a nun and holding a napkin that had written on it "You don't want to play with me any more?"
Note that I have replaced draped with by draped in. The reason is that draped with is used to describe some sort of decoration, for example,
The Christmas tree was draped with tinsel
draped in can also be used for this, but is usually used when a person has something wrapped round them and is effectively wearing it.
It flaunted a digitally modified photograph of five men—West Bengal Chief Minister Buddhadeb Bhattacharjee and his top four administrators—draped in colorful saris. Pluralism and Democracy in India: Debating the Hindu Right
For a blanket, draped in is the more appropriate term.
Of those two choices, only that had written on it is grammatical.
Something that uses on which had been written . . . is another choice, and some people will this is correct while the other way is not. However both are grammatical with this one being quite formal.
I assume that you don't know--or don't want readers to know--who wrote it. If we do know, then a more simple style might be easier to read, for example: on which she had written. You might also consider napkin, on which had written, xxxxxxx.