The DMCA covers copyright, and only copyright. It is the right instrument when an infringing page has copied a brand's photographs, code, or written content, which phishing clones almost always have. It is the wrong instrument for a trademark complaint, and filing it as one is a common reason a notice is rejected.
A valid notice has required elements: identification of the copyrighted work, identification of the infringing material and where it sits, contact details, a good-faith statement that the use is unauthorised, and a statement of accuracy made under penalty of perjury. The last one is why a DMCA notice is signed by a person, not generated by a tool.
Its force comes from the safe-harbour bargain. A qualifying provider that removes the material expeditiously keeps its protection from liability; one that ignores a valid notice risks losing it. That is what turns a request into something a provider acts on.
The recipient may forward a counter-notice from the person who posted the material, which can restore it unless court proceedings follow. In practice fraudulent operators rarely counter-notice, because doing so means identifying themselves and accepting jurisdiction.
How Fraudox handles it
Fake page takedown