Rinsing the mouth with water after fatty drinks (and foods) means you are reviving a sunnah!
Water and siwaak: why?
Al-‘Utahymeen said: The reason why the Prophet, peace and blessings be upon him, rinsed his mouth was because of the fat. It can be understood from this action that it’s legislated to rinse the mouth from all foods which contain fat, regardless whether drank or chewed. It is good manners to rinse the mouth afterwards to remove the fat. If the substance is heavy in fat, then it’s better to use siwaak. For this reason the scholars say: it is sunnah to use the siwak to remove any fat after eating if the smell of the mouth changed. [Sharh Saheeh Al-Bukharee]
Remind yourself and others, in shaa’Allah!
And remember: Whoever revives an aspect of my sunnah that is forgotten after my death, he will have a reward equivalent to that of the people who follow him, without it detracting in the least from their reward. [At-Tirmidhee]