Well...my stock answer would be honesty. But I don't think airlines have any access to military records other than your DD-214 which would only show wings, air medals, and codes to indicate certain quals. Of course your service reputation might or might not become known to people at certain airlines...

Airlines are usually interested in failures of a checkride which would result in an operating privilege if passed, and less interested in the details of a long training program.

I would think phase graduation checks and things like AC or SL checkrides might be the same as as FAA checkrides in that sense. Downs and the like would probably be less significant.

Maybe pose the question in the military forum and see what others have been asked at interviews?