Trump attacked Amazon because of business; he seems to think Amazon is profiting from the US taxpayers' money.
Now Amazon has a strong financial incentive to go to court in this case as winning can lead to potentially securing a 10b$ contract. Whereas losing costs maybe some millions?
Both Bezos and Trump are very pragmatic business men. I think this is all just about money.
If you really thing Trump dislikes Bezos because of "profiting from the US taxpayer" instead of "owning The Washington Post", I don't even know what to say.