Sheep fins are good for fostering children. The sheep have been genetically combined with fish, so the sheep have fins (and they've lost their tails - which is why the tail part of the sheep radical is missing in this kanji!). These sheep fins are very rich in nutrients and as such are very good for foster children that need to grow up big and strong.
The best way to foster a better relationship with these foster kids would be to give them some yogurt (よう). Maybe they can dip the sheep fins in the yogurt to help mask the strange taste. Yogurt is also very nutritious, so it’s a good supplement to the foster kids’ diet.