I noticed a slight clicking noise and a resistance when squeezing the right (from the bicyclist's point of view) brake. Inside the hood, I can see a white rubber thingy (pivot bushing, thanks mikes) that has come half loose. The pictures are taken from above, when squeezing the brake levers as far as they can go. On the left brake, the white thing sits nicely in its slot. To the right, it has come loose and moves around weirdly and makes a noise.
Is there a way to get to the bushing and put it back in its place? I feel that some disassembly is required.
I have a pair of Shimano Sora brake/shifters, manufactured in 2015:
UPDATE: Turns out the thing the pivot bushing sits in is called a "brake cable hook"!