Dial calipers have a rack which meshes with a gear that drives the pointer. Sometimes the gears jump a tooth or more, resulting in the pointer not reading zero when the jaws are shut. I am guessing, here, but the tool may be for tipping the spring loaded gear out of mesh with the rack, to get the pointer reset. I had a Tesa dial caliper, but that was 40 years ago, and my memory is not great.
Somebody will be able to post some photos showing exactly how its done.