If for the 56 Ford, yes there is a special tool for it. Maybe some one here has a picture they can post. Absent any other name, it is an Inside Door handle removal tool.
fyi these clips are called "jesus" clips in the trade because they have a habit of flying away. the straight style clip remover they sell in autoparts stores is to narrow to fit around the handle if you can find the ones pictured above or modify the other or a dental pick will also work just be careful of the flying clip. also there is a spring behind the panel pushing behind the handles so it may take some effort to get the tool behind the handles.