Yes. It could be seen as an elliptical sentence, thus: "They let her go out anytime (she wanted to)." In any case, it's fine as is.
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an·y·time
adv.
At any time.
Source: The American Heritage® Dictionary of the English Language, Fourth Edition
Copyright © 2000 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.
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