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A phrase coined by the voice actor Hikasa Youko, a combination of the onomatopoiea "tehe" for giggle and "pero" for sticking the tongue out.
It is often rendered with a star 「てへぺろ☆」; the full emoticon is 「てへぺろ☆(・ω<)」, from her 2009 blog post
The archetypical facial expression and pose for tehepero incorporates a cheeky grin with tongue out, a wink, and either one arm up behind the head (the K-on! version, see post #784089) or a v hand sign raised to the face (Hikasa Youko version, see photo of her on Koyama Tsuyoshi's twitter)
The pose is usually used in the Japanese pop culture as a way for the character to cover their mistake and brush it off with a cute expression.
Since winking and sticking the tongue out are both common facial expressions, an image should only be considered a reference to tehepero and tagged as such if the complete tehepero pose is emulated, or if a reference is made explicitly in text (i.e. 「てへぺろ」 in speech or sfx). If the character is tapping their head while winking and sticking their tongue out, use dojikko pose instead; if they're touching their head with both hands with both eyes closed, use ah eto... bleh (meme).