@Red225 Retaining them would leave questionable entities within your organization. It is not something you'd want. But you're right that it'll solve the immediate manpower issue.
As for reputation: Execution would be too far, the common punishment for something like this would be to throw them into the dungeons and have them rot there. While you might believe that is still too much, it's important to remember that these are subjects serving a lord. Not citizen employees working for merchants or whatever. Their families would not associate with them, and defending them would further ruin themselves, because publicly, their crimes are clear and they acted against a decent lord, which disgraces them further. Based on their jobs, it's safe to assume they're not of high standing, so they do not have the authority or influence to cause trouble. Major enemy houses will not take the risk to support them, because frankly, they have no value, and they're within MC's territory. It is also not easy to migrate to another territory in such times. If by chance, they managed to reach another noble's lands, they also won't necessary be hired, even if it's a faction hostile to MC's house, because while it's useful to gather people that hate your enemy, it is more important to not associate with disgraced individuals, especially ones that have outright defied their lord.
So, to the public, it'll just be a few lesser nobles/commoners committed a crime and got sent to jail, case closed, forgotten.