Although way back in 2008 I wrote about complete and accurate (here), yesterday I realized that I hadn’t written about use of completely as rhetorical emphasis. So I exhumed the following corpses from EDGAR:
In addition, all financial data must be completely and accurately recorded in compliance with applicable law and Invesco’s accounting policies and procedures.
… the Executive agrees that he will keep the terms and amounts set forth in this Agreement completely confidential …
… the Adviser and the Trust acknowledges that the Sub-Adviser may suffer irreparable harm for which monetary damages may not be completely adequate …
The Executive will keep full and complete written records (the “Records”), in the manner prescribed by the Employer, of all Inventions and will promptly disclose all Inventions completely and in writing to the Employer.
I suggest you can safely omit completely from each. (In the first example, you can get rid of accurately too.) That’s because it’s rhetorical emphasis—all it does is wag a finger in your face without affecting meaning.