No. Equifax cannot remove a credit blemish that is correct and real. Equifax has not messed up. The problem is on your end, between you and the creditor, not between you and Equifax. Equifax is simply a reporting repository for their member companies, who report their credit dealings with the member's customers.
You need to correct the situation, and ask that the company then properly report the fact that the account is satisfied, and now pay in full. It will still show as paid through collections, but will turn a blemish into a positive, which will improve your rating over time, especially if the account is NOT closed.
Equifax cannot do as you request, as it's a falsification of their reporting records. It would also undermine their credibility as a trusted credit reporting agency.