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You don't need the commas in that sentence. Instead, it should be, "Jill gently took the box out of the cupboard." (The word "gently" doesn't work well there. Use "carefully" instead.)
You could also put the adjective at the end of the sentence. I agree with Ron that there is no need for the commas. We put commas around adverbs like 'surprisingly' that express opinions about the whole sentence, not adverbs of manner.
punctuation 
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