You can't proactively perform the debit, but you are not prohibited from bringing the facts to the consumer's attention.
Here's what you can do. Send a letter or make a call that:
1) Details how you issued credit because of the claim that was previously made;
2) Explains how a merchant credit has now come through that "appears" to resolve the dispute (the credit may be for the same amount but you don't know why the credit is there - it may be for another purchase or even for a purchase on another card).
3) You are requesting that the consumer contact you via phone and/or mail in order to discuss the dual credit.
Provide as much detail as possible (dates, amounts, ect.) Mention nothing about wanting to re-debit the account. A reasonable person would contact you to have the dual credit removed. If the consumer decides to not contact you, then there isn't anything you can do.
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My opinions do not necessarily reflect those of all the voices in my head.