Hungry Imps want a specific type of food. The food that they want will be displayed as an icon over their head.
After you collect the food that a hungry Imp wants, equip it in your primary equipment slot then go near the hungry Imp. Tap and hold on your Scout, drag away from where the hungry Imp is standing, then release to throw the food towards them.
Imps tend to pick up the items we throw near them, so be careful when throwing the food to a group of Imps where the hungry Imp is standing, as other Imps might take it away from them.
The icon above a hungry Imp will change to a heart after they have been fed. Interact with them to receive a reward.
Please note that you may need to gauge the strength of your throw relative to where the hungry Imp is standing. Also, be careful not to get too near the hungry Imp as they may run away from you.