D-IFF_ident, no doubt someone deep and blunt came up with that nonsense. Presumably you would also be required to declare any free drinks, in-flight entertainment and similar which you were given on-board as 'entertainment'?
The process of 'handing-back' air miles would be an administrivial embuggerance of indescribable pointlessness and would be a complete waste of everyone's time.
I suppose if petrol stations still gave away Green Shield stamps or free glasses with 4 gallons, you would have to hand those in to Their Bluntnesses if you had to fill an MT vehicle up from a civvy pump.
Here's another one. Let's say that you choose to pay for a meal taken in the course of duty with, for example, a Lufthansa Miles-and-More Visa card rather than faff about with cash. The card gives you 1 mile per €1 spent - would you have to 'hand in' the miles earned to some blunt fool?