Does working in a job obtained in an undeserving manner, and repenting from this action, make continued work unlawful, and must it be abandoned for the repentance to be valid?

Cheating is forbidden, and "whoever cheats us is not of us." Cheating in competitions is worse because it leads to unqualified individuals assuming positions. If a person cheated in a competition and obtained a position they would not have otherwise, then if they repent and are qualified to perform the work, it is permissible for them to remain in their position. This is because choosing the most competent is not a condition for the validity of assuming a position; it may be permissible to appoint a less qualified person even when a better one exists. So, if you are proficient in your work and perform it as required, and you have repented from the error of cheating, there is no harm in you remaining in your position.