if you want to make a damage claim then you should do it before your next guests arrive or within 14 days /I think). In that case, you contact your guests first, ask them to pay and if they refuse or ignore it then you involve Airbnb.
If it's too late and you already have new guests then you can't get any money for the damage anymore so there is no point to contact them now. If they wanted to pay they would tell you about the damage and offer to pay immediately.
Slam them with an honest review and 1* rating and hit the "I wouldn't host them again" button and maybe you will save another host