1. What does it mean?
드립 is shortened from 애드리브. 드립을 치다 means to make a joke or riff, while attaching 드립 to a topic can frame what someone says as a predictable line or excuse.
Also written or said as 드립치다, deurip
2. The nuance
It is not the English Gen Z fashion sense of 'drip' in this use. It can be funny or dismissive, and saying 농담이야 does not erase an insulting impact.
3. Examples
“포장지를 보더니 말장난 드립을 쳐서 다 웃었어.”
They made a pun about the wrapping, and everyone laughed.
“진지하게 하는 말을 또 드립이라고 넘기면 서운하지.”
It's hurtful when a serious point gets brushed off as another joke.
Sources
References support the meaning and usage. Example sentences are written for NoCapWiki.