Is there any diplomatic effect for "You'll pay for this" responses when talking to other players? [duplicate]

When being told

Oopsies, it seems we have squashed one of your favorite city-states.

or similar niceties by an AI opponent, is there any diplomatic or other effect for responding with "You'll pay for this" or the nicer option such as "We won't let this divide come between us"?

The dialog choices seem to offer a chance to shape the relationship with the other leader. However, the diplomatic tooltip hints never mention the responses.

Solution 1:

Seems likely to me that it will help to raise tensions; which in turn might have it's uses. Like luring them into declaring war on you so you can thence crush them and still look like the good guy in front of other players/city-states, or maybe milk a defensive pact.