1. What does it mean?
어쩔티비 is a meme-style retort used to brush off another person's comment. Its point is the teasing, unbothered sound rather than a sensible statement about television. People sometimes extend the joke by substituting other appliance names.
Also written or said as 어쩔TV, eojjeoltibi
2. The nuance
It may work as mutual childish banter, but easily sounds rude or evasive. It is especially unsuitable when someone is asking a serious question or explaining a problem.
3. Examples
“친구와 장난치다가 어쩔티비라는 답장이 왔어.”
While we were joking around, my friend replied with a childish 'so what?' meme.
“진지한 질문에 어쩔티비라고 하면 대화가 끊기겠지.”
Replying with that dismissive meme to a serious question would shut the conversation down.
Sources
References support the meaning and usage. Example sentences are written for NoCapWiki.