Is it gratitude pets feel for those who take care of them? Some believe their pets love them. Are they right or wrong? How can we know?

The mistake here, I think, is to consider pets as some kind of reduced human. They are not. They are of their own kind. Dogs, a pack animal, will have a totally different relationship from cats, a pairing animal. And neither is a human, a socialised primate. One can conjecture that dogs feel loyalty to a pack leader who provides capable. Cats will rather see a partner - perhaps a more capable one, but nonetheless an equal in principle. Where gratitude comes into it is more debatable. When you have a pleasant dinner with your friends, do you feel gratitude? Because that is possibly the way cats feel toward you. When you pass the professional exams and get a raise in grade, do you feel gratitude towards your boss? Because that is possibly the way dogs feel toward you.