Decay happens faster earlier in the game and slows down as the game comes to a close. You can’t hold a war from the Ancient era over another civilization more than a thousand years later. When in a period of peace, the number of grievances will slowly trend toward zero. Possessing another civilization’s city generates a small number of grievances each turn. Ignoring a civilization’s request, such as not settling near them again, will also give them a few grievances to work with. Taking out a city-state will give all civilizations (at least those that have met them) grievance against you. These include denouncing another civilization, declaring a war (surprise or otherwise), and capturing another city. They are a way of penalizing players for acting in ways that are not good for world peace.
Grievances have replaced the warmonger system. Our Civ 6 Diplomacy guide will run down each of these features and help you understand it. Warmongering has been replaced by grievances, a diplomatic victory option has been added, and the World Congress is back, supported by diplomatic favor. One of the biggest changes added in Civilization 6’s Gathering Storm expansion is an overhaul of the diplomacy system.