Oh my god. That mental image just made me burst into laughter.
Hm...After TF2 was over? I've got a shitload of different headcanons for this. One goes where the wars go on and on forever, and signing a contract is essentially signing a death sentence. A computer will retire a man, but he will never leave the battlefield. New teams are brought in periodically, but no one ever really thinks about what happened to the old teams.
Another headcanon is that all the mercs get fired, and they all split off in their own directions, but it's actually really sad, because the only place they belonged was with each other, and they eventually meet up again and go to fight godzilla and shit
as the A-Team together.
And yet another is that it's a nine-to-five job, so when it's over, it's over. The guys find other work, or move off to Australia to fight kangaroos for the rest of their lives or just do whatever they want. Nothing really comes of it--they're just not together anymore.
As far as the whole MvM thing goes, I figure they just go in, kick Grey's ass and are done with it. After that, the Admin does some handwave thing of 'oh yeah you're not all really fired' and the fighting continues, but this time the teams aren't really sure who they're actually working for, just that they get a paycheck every month to kill someone wearing a different colour than them.
I've probably got more but I'm not gonna spam with that crap.