I accidentally hit my parrot while trying to open a chest, but when I offered them some wheat seeds, they wouldn't eat them to heal up. I was only given the "Sit" and "Stand" options, and no "Feed" option. When the same thing happened, except with my dog, I was able to heal them by feeding them some cooked steak. Same thing with one of my cats, except with raw salmon to heal them. 
It also applied to both of my parrots, which led me to accidentally killing one while going for the anvil behind them so I could apply Unbreaking 3 to my diamond helmet. 

While I understand I could've healed them via a splash health potion, healing them via the seeds should've worked just as well. I also tried healing them via melon seeds, but they didn't work either.