Skye likes routine and eggs.
Every evening when it's time to put the chickens to bed, we prepare them some treats which includes their hardboiled eggs. Skye who usually doesn't care much about what's going on in the kitchen always appears at that time. She also gets a little piece of egg.
Since it's of high value to her, we use it to reward/reinforce things we want. At the moment, we want her to make a good association with Peter. Despite all his love, patience, and playtime with her, Skye is still a bit weary about him. So Peter is the one to give her this egg treat.