I fed the crying imp a chocolate heart and it didn't give me a reward! (Cozy Grove)

This is actually correct. There's an intentional little mystery here, and simply feeding the imp a bon bon (the chocolate heart) isn't the full answer. Scoutmaster Blake's letter on Campaign Day 21 hints at what's going on. If you don't want to try to figure it out for yourself, you can read the explanation and spoiler below (i.e., stop reading now if you don't want to know more, or scroll down if you do want to know more).

We use the term "heartbroken imps" for these imps that are crying and ask for bon bons. Unlike imps that ask for other objects, it doesn't matter how many bon bons you feed to a heartbroken imp. What you have to do is find two heartbroken imps on your island. Throw a chocolate heart such that one of the heartbroken imps will run to it and eat and, after eating, be a bit closer to the other heartbroken imp. Do this repeatedly to bring the two heartbroken imps closer and closer together. When they get very close to each other, they should see each other and have a red heart overhead. Then you can talk to them for a reward.

• Note: As of version 5.1.0 there's still a longstanding bug where sometimes one of the heartbroken imps won't spawn. So if you see a heartbroken imp and want to help it, you should first make sure that there's another heartbroken imp on the island, AND try to help them in the current play session because imps can reset (and thus might no longer be there) each time the game is loaded or the island is regenerated.