Counter-Notice
Quick answer
A sworn response by someone whose content was removed via a DMCA notice, asserting the removal was mistaken and requesting restoration.
After a counter-notice, the original complainant has roughly 10–14 business days to file a court action; otherwise the platform may restore the content. Counter-notices are signed under penalty of perjury and disclose the filer's contact information, so they should only be filed by parties who genuinely hold the rights.