If I were the planning staff for that operation of the CSG&M, I would go with a full false flag operation. So, there are pirates, whom I payed and provisioned to harass the Lyrans and now they turned on me? Well, that just sounds like a job for the Lyrans and theire mercenaries to do. So here is how this would go down in my head.
Note, during that time ComStar controls the mercenary business and, of course, FTL communications. Also, ComStar has the best code crackers, ROM, and basically reads all communications of all people in the known 'verse. So, faking communication protocols and proper usage of codes as well as complete IDs should be a cakewalk for them.
Thus, I would assume, they created a mercenary unit with some fake history - not too specific, just credible enough - and design a LCAF handler for them, just on paper of course, though a face in ROM should exist, just in case. Then let these mercs, who are of course CSG&M personnel, eradicate the pirates and receive proper payment from the LCAF handler. This should be noted with the The Mercenary Review Board, but probably the paper work should stop there as not to arouse LCAF suspicion. Alternatively, construct a minor Lyran noble and let him / her pay for the operation, making this a private venture and hence having less paper trail.
The important part is, all leads this possibly creates are red herrings. Nothing leads back to ComStar, and all trails point toward a regular, run-of-the-mill peripheral pirate hunt done by some unimportant mercs and financed properly, taken care of by a handler with solid paper work and paid for seemingly by a legitimate account.
The CSG&M mercenary outfit should apply regular camouflage and some merc logos. That's it.