Modern Employment Reform, Improvement, and Transformation Act of 2022 or the MERIT Act of 2022 This bill revises provisions related to federal employment, including the furlough and removal of federal employees, the calculation of federal employee retirement benefits, and the length of the probationary employment period. Specifically, the bill repeals the process for taking action against a federal employee for unacceptable performance, accelerates the process for removal or suspension based on performance or actions, and prohibits grievances based on adverse personnel actions and reductions in force. The bill also authorizes an agency to remove a senior executive from the civil service for performance-related reasons, and it revises provisions covering performance- or conduct-related actions against senior executives. The bill authorizes agencies to furlough employees for such cause as will promote the efficiency of the service, and it prohibits appeals to the Merit Systems Protection Board based on short-term furloughs or furloughs due to a lapse in appropriations (i.e., government shutdown). Additionally, the bill limits the retirement benefits of a federal employee who is removed due to a felony conviction related to their official duties by prohibiting felonious service from being taken into account when calculating the employee's annuity. The bill also authorizes an agency to order the repayment of a bonus or award when performance or conduct issues are discovered and such bonus or award would not have been paid had such issues been known when they were made. Lastly, the bill extends from one year to two years the probationary period for competitive service appointments and members of the Senior Executive Service.