An elderly woman admiring a festive Bergdorf Goodman holiday window display in Midtown was pickpocketed by a brazen grinch with a long rap sheet, cops said Monday.

Elijah Gay, 23, snuck up behind a 77-year-old woman on Sunday and allegedly swiped her wallet as she gazed at the holiday window display around 2:41 p.m. on Fifth Ave. and West 57th St ., police sources said.

Workers at the high-end clothing store tipped off cops that someone appeared to be casing people outside the building, cops said. Officers at the scene then saw Gay allegedly pickpocket a 79-year-old woman around 3:45 p.m., cops said. The officers followed Gay into a nearby train station on West 57th St. and Sixth Ave., where they took Gay into custody.

Police recovered the 79-year-old victim’s wallet, which contain

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