They actually make a few different tools to remove these. The most common looks like a long slot in a piece of sheet metal. The idea is to insert this release tool between the handle and the escutcheon plate. The tool is generally inserted in the direction where the tool is beneath the lever part of the actual handle (assuming the C-clips were put in right, if they were ever apart). The tool fits into a groove in the inside door handle, and as it is pushed further onto the door handle shaft, it releases the C-clip and the door handle simply pulls off. Sometimes the clips have been installed backwards, in which case, insert the tool with the lever part of the door handle facing away from the tool. Another common tool for releasing the C-clips that hold the door handles in place looks more like pliers, but rather than having a pliers-type end, it has flat, hook-shaped blades on the end. Simply insert the tool behind the handle, press in to grab the C-clip, and pull out.
Do an internet search for “Door Handle removal tool” and you’ll see both of these types available. In some cases they are a real pain, and it helps to get a friend to push in on the inner door panel while you negotiate the tool into position. Have a nice bright flashlight available too, as once you get everything pushed back, often you can see the clip itself.
I have used both types of these tools to remove inside door handles, but find the pliers type to be the only one that works well for me on GM cars of the ’30s. I have used both with success on ’40s and newer cars. Take your time and be patient with it; once you get one, I assure you the rest will come easier. If that clip pops off to places unknown, they do reproduce them and they’re relatively inexpensive. Let me know how this works out for you!Wrench Safe, Mark