The Dane has joined Barca in an €18m deal as an emergency replacement for the injured Ousmane Dembele.
But the whole affair has infuriated Ortega, with Leganes denied the opportunity to buy a replacement themselves.
"We do not understand that a team, because a player has been injured for a long period, can unilaterally transfer this problem to Leganés," he blasted.
"We would understand if the regulations allowed an exceptional authorization to Barcelona to sign by mutual agreement. But not in the way as it was done, with the payment of the clause unilaterally.
"The current regulation goes against the integrity of competition and the right that all clubs have to compete on equal terms.
"It is almost irreparable damage, but we will use all means to counter it."
Despite his fury, Ortega insists Braithwaite leaves with their respect and best wishes.
"He has been a great professional. Yesterday [Wednesday] he came to say goodbye to all the club staff and to inform us about the situation. We wish him the best of luck."