My answer is different from everyone else.
IMHO, the league will deal with this in a bifurcated approach. Two prongs.
Prong one.
Officially they will deny that there is anything wrong, they'll underscore how important the competition is and how difficult it is to build a winning team, and defend the league and its teams, including the Dolphins, but not specifically praising the Dolphins. They will threaten extreme consequences if anyone were to tarnish the shield by choosing not to compete. They'll talk about how it would be almost impossible to go against the motivation of everyone involved in the process, and even if someone tried it, the chances of getting the top pick would be almost impossible. Too many variables. Dismiss it, deny it, sweep it under the rug, refocus the conversation to the more important issues of the league such as Super Bowl location selection, Draft location selection, unparalleled parity in the league, and if things get to intense, even the CTE controversy.
Prong two.
In privet the owners KNOW that teams tank, and it's tacitly allowed. But, they'll reprimand Ross and tell him to get his house in order to make it less transparent. They'll throw their weight around to Ross personally, and make certain that Ross takes actions with his house to ensure that it is less obvious and that he fields a more competitive team … or else there will be consequences. THIS will cause instant reverberation for the Dolphins, hard language from Coach Flo about consequences for people who do not do their jobs, rare interview "on the run" with Grier as he moves from point A to point B so he only has a minute for one question, no follow up, and Grier talks about how ridiculous these allegations are and how his job is on the line just like every other GM and if he doesn't produce wins he gets fired. He'll talk about how GM's rarely get the credit when the team wins and how they always get the blame when teams lose, nervous laughter, and he'll make a strong assertion that this is not happening here and that we're building something great … then he'll have to go.
That's how I see the NFL handling this … let's see how this plays out.