Is it permissible to re-engage in binary options with the intention of recovering only the amount I lost, knowing that trading in them is impermissible?

Binary options trading is impermissible because it is considered a religiously forbidden gharar (uncertainty) transaction. It is not money, nor a usufruct, nor a financial right that can be exchanged for compensation. It is not permissible to engage in a forbidden transaction under the pretext of recovering previous losses.