What must be done after the Captain resolves a mechanical irregularity found post-flight?

After the Captain resolves a mechanical irregularity found post-flight, it is essential for the Pilot-in-Command (PIC) to formally close out the flight again. This process ensures that all discrepancies, findings, and any actions taken to rectify the irregularity are documented in the flight report. Proper closure of the flight is crucial for maintaining safety and accountability in operations, as it allows maintenance and operational teams to have an accurate understanding of the aircraft's condition and its airworthiness status. This also helps in tracking any recurring issues that may arise with the aircraft, contributing to long-term safety and reliability.

The other options do not encompass the necessary actions required after resolving a mechanical issue. Seeking only flight crew approval does not provide the formal documentation required, and while submitting a report to operations can be part of the process, it's not the immediate step to close out the flight. Simply assuming no further action is needed undermines the importance of taking comprehensive steps to ensure safety and compliance with operational protocols.