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You need to follow the counter-notice and put back procedures laid out in Sec. 512 of the DCMA. Once you provide a proper written counter-notice stating the material does not infringe copyrights as claimed, the service provider has to promptly notify the claiming party of the your objection. If the copyright owner doesn't file a lawsuit in district court within 14 days, the service provider is required to restore the material to its location on its network. [512(g)(2)(C)]
By far the most useful internet resource I've found is chillingeffects.org which is a project of the RFF and Harvard, et at. In additional to explaining the legal ins and outs of online rights in as much detail as you could want outside of law school, they have a form you can use to prepare a proper counter-notice. I have it bookmarked.
You can fight them in court, according to Kelly/Warner Internet Law & Defamation Practice:
"What many who abuse the DMCA system do not realize is that they can be sued and held civilly liable for the havoc they wreak by sending these fake notices.
"A perfect example of this is the case of Online Policy Group v. Diebold, Incorporated. Diebold made voting machines used in US elections. Online Policy Group was critical of Diebold’s machines, and released e-mail correspondence from the company that they had obtained onto the Internet. Diebold sent DMCA takedown requests to have access to the e-mails that Online Policy Group had posted online removed.
"Online Policy Group sued Diebold over the takedown requests, arguing that the Group had the legal right to publish the e-mails. A California court agreed with the Group and granted a request for summary judgment, after which Diebold settled with the Group to pay $125,000 for their monetary losses and legal fees. The case was just one of many which have been fought over unsubstantiated DMCA takedown requests.
"It is also important to remember that, even if someone is willing to risk these civil damages, there are also criminal sanctions available for false DMCA takedown request senders since the requests are sent under the penalty of perjury."