it's gibberish, but it's the kind of gibberish that's common in the pinkyworld to make it sound more complicated and significant than it is.
when you buy back shares you hand them over to the TA with a copy of the board resolutions authorizing the buyback, an opinion of counsel saying the buyback was effected in compliance with law, the company's governing docs and the board resolutions. and a determination, also conveyed to the TA, whether the shares are cancelled or retired to treasury. the only think you and your TA have to check with Cede is to determine which shareholders match the shares you bought back.