The woman was part of a tour group which stopped in Queenstown and Arrowtown before travelling to Milford Sound and staying in Te Anau.
The woman was arrested at 9pm on Wednesday by Te Anau police.
A CCTV video clip of the woman putting the piece by Queenstown artist Alison Naylor into her bag received widespread coverage.
After paying the quilt's value of $625 in reparation, which Ms Naylor will receive, the woman was released with a pre-charge warning.
Ms Naylor, who has five other works on display at the museum, said she was just pleased the woman did not take one which had already sold or the one which had been given to her son for his birthday.
''I just tell all my friends that mine was the most appealing,'' Ms Naylor said.
