Did the eBay seller produce a receipt for the (alleged) CLA? I suspect (not fact, just suspicion) many a seller fancy themselves as camera repair people: removing the cover, greasing a few points and calling it a CLA. I've been duped like that myself (when asked, the seller admitted to performing the service himself and not having any speciality in it). You could record the speed variations and adjust your shooting to match but -- REALLY?! -- this is a new camera to you. I have an M4P and had it serviced and it functions wonderfully. Just like the even-older M3 (CLA'd as well). On a professionally serviced Leica, the age doesn't matter as it can be essentially restored to new mechanical condition.
You should consider contacting the seller and seeing if he/she will offer to pay for a professional CLA for you or you should consider returning the camera. A full CLA would run between $250-300, depending where the work is performed.
Best of luck!