Loose brake cable hook bushing inside the brake/shifter hood

Question

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.

Another picture, further away and from the front of the bike:

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"!

Answer 1

The little piece is the pivot bushing for the lever shaft. Its' job is to prevent a metal on metal contact point. You can reposition it by loosening the cable clamp at the brake caliper, gently slide the little barrel out far enough to install the bushing. By pulling the cable back every thing should go back in place.

It can be helpful to have a pair of needle nose pliers nearby, as you might need to pull the cable a bit to make the barrel move far enough. Also, if possible, move the shift/brake lever inwards towards the middle of the bike before closing the brakes to open up the hood as much as possible.