after New Year's Week; after the New Year's pine decorations are removed
Refers to the period after January 7th (or 15th in some regions), when the traditional kadomatsu (pine decorations) are taken down, marking the end of the main New Year's celebrations.
By the time the New Year's pine decorations are gone, the festive mood has already faded.
I took a walk through the quiet shrine after the New Year's Week.
Compound of 松 (pine, referring to the New Year's kadomatsu decorations) and 過ぎ (passing, after). The exact historical derivation is uncertain, but the word is conventionally associated with the end of the New Year's celebration period.