Rework Food packaging (Glass bottle manufacture)

Quick question, if we hold product for any type of critical error (birdswings, chips, wings), we would hold three (one before, current, and one after the defect was found). The held product is then sent to a 3rd party to resort (check every piece) before going to our customer. Would that resort process, even though it is not done in our facility be considered rework? What would your idea of rework be? 

do you get the product back?

Sometimes it ships from there and sometimes it will be sent to a storage facility that is owned by our company.

has it already been issued a lot/batch when you send it to be sorted?  If so, yes that is rework as you will have less when you are finished than you originally thought.......so you have to track it as rework to be able to "write off" the damaged pieces

If not, then no, I wouldn't consider it rework at all

if you don't log that activity as rework, then technically it doesn't exist and you have no paper trail.............it gets shipped out but doesn't really exist

Make sense?

Makes total sense, Thank you!!!