Is it permissible to supplicate against a foreign woman with whom one had an illicit relationship and committed adultery, after the supplicant regretted it, detested the girl, and claimed strictness and jealousy to justify distancing himself from her?

You are obliged to repent to Allah Almighty for the illicit relationship you engaged in, which resulted in committing fornication. It is not permissible for you to supplicate against her, because if she is a Muslim, then supplicating against a specific Muslim due to their falling into sins is not permissible, as the Prophet (peace and blessings be upon him) forbade it by saying: "Do not say such things; do not aid Satan against him," and instead, "Rather, say: 'O Allah, forgive him! O Allah, have mercy on him!'" And if she is a disbeliever, a specific disbeliever should also not be supplicated against, because it is unknown what Allah will seal their life with, as they might be guided. Ibn al-Arabi said: "As for a specific disbeliever whose end is unknown, one should not supplicate against them, because their ultimate fate is unknown to us."