Many types of green worms affect
apple trees.
These include several species of moth larvae called leaf rollers.
Leaf rollers
feed on the leaves of the tree, causing the leaves to roll up from the damage.
Another type of moth that produces a green worm that infests apples is the green fruit worm.
Green Fruit Worms attack both the leaves and fruit of
apple trees, and can cause damage to crops.
At least 10 different species of green fruitworm have been identified.
Many species of Geometrid moths also produce green larvae that are called inchworms.
They have a characteristic 'inching' movement and enjoy feeding on apple trees.
This rolled leaf will often be used as a home for the worm, held together with silk.
Saw flies also produce green worms that will feed on apple trees.
Saw fly green worms will feed on the leaves and fruit of apple trees, often boring several different holes into the same piece of fruit.
The California pear saw fly and the Dock saw fly are examples.
Other than the methods already mentioned above for control.
You could use DE (
diatomaceous earth, food grade) just dust the tree trunk and leaves with it. (don't breather it in, it can do serious damage to lung tissues).
By dusting the trunk, and perhaps the ground around the tree trunk, you can stem any larvae from climbing up a tree trunk.
The dusting of the leaves will help keep the egg laying moths down. Do be aware that any beneficial insects will also be affected by the DE.
Soapy water used in a low pressure sprayer (I like a hand
pump up 2-3 gal. model) will be effective in washing off the eggs as well as the larvae.
The larvae in your photos appears to be a green fruit worm.