Is there a way to filter the burned items study to only go over Kanji?
No, there’s not. I was actually thinking about this the other day: if there was an option to review only burned radicals, kanji, or vocabulary, and an “all” option.
You can do this if you use the script Item Inspector for reviewing your burned items. Just add an Item Type filter to the Burned Items table.
The self-study userscript should be able to do this, even if you have problems doing it in WK proper.