Kermit's tea cup was a common fixture on The Muppet Show, often seen on Kermit the Frog's desk, backstage.
Since this time, tea cups (or sometimes coffee mugs) have occasionally been an accessory for Kermit in other media, either in association with The Muppet Theatre, or other uses such as the popular "tea lizard" meme that spawned from a 2014 Lipton commercial.