But officials aren't sure the person in the photo actually stole the 20-kilogram (44 pound), century-old sculpture.
The gilded bronze item was part of a statue outside German cookie baker Bahlsen's Hannover office, and it was reported stolen last month.
The Hannover police's statement says a local newspaper on Monday received a picture of someone dressed like the Sesame Street character holding what appears to be the stolen cookie.
The enclosed note is written in cut-out letters.
An earlier letter demanded that cookies be delivered to children at a city hospital, but the new note made no demands.
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