If a decision by the EPSO Selection board is considered to be unlawful, candidates can submit an appeal or a complaint against such decision based on the Staff Regulations of EU officials (e.g.. if the selection board has not accepted a diploma or other qualification as relevant to the exam profile and consequently disqualified an applicant). The European ombudsman also receives claims but those are limited to maladministration, which essentially means that the candidate challenges the rules rather than the individual decision.
See also:
Staff Regulations, Selection Board