There is a technique for removing barbed hooks from flesh. As used by the water warden in the pics above.
Holding the eye of the hook firmly down onto the flesh, pass a length of strong nylon or cord under the arch at the bend. Give the nylon a good quick and hard tug along the arm/finger,and it will pull the barbs out.
It does work and I have since seen it used successfully elsewhere.
Not used those but I have used the method that they rely on - basically you put a loop of nylon behind the bend of the hook and pull the hook sharply backwards with it the way it went in. It creates a bigger hole that when it went in because the barb catches but it quick and efficient.
The trick is to pull parallel with the surface it's hooked into and, if you can, push down on the point and barb to keep everything in a straight line.
Placing a stick between the victim's teeth prior to the operation is optional.
The other way is to twist the hook up so that the point and barb come through the skin again making a second hole. You then cut the hook behind the barb with wire cutters and pull the rest of the hook back out.
Both work, the fist is quick and certain, the second requires a bit more work and determination from both parties.
The doctor at St John's hospital told me when a hooks buried deeply into your finger "like that" you can easily cause nerve damage pulling it out.
I was hooked down to the bend and into the bone, I'd tried to pull it out before it got tender but I couldn't budge it, it's surprising how firm a hook can feel when it's stuck in your index finger.