As far as is implied, if you send them on a mission that could fail catastrophically, or if they fail too many times in certain ways, then they can develop a negative trait. As for getting rid of the trait, I don't think it is possible, though I wish it was possible. I would suggest sending them against whatever caused the problem and hope they succeed enough.
If that doesn't work though, then I would suspect that there is no way to remove a negative trait which truly is a very annoying aspect of the strike teams.
I tried with a strike team that had a negative trait for a short time, but I am not a big fan of passive mission systems for some games, so I just gave up on the strike team and retired them. It's been expensive as I have had to retire a second strike team and a third strike team. At least the replacements don't look like crappy teams.
