Theoretically, the agency involved in 'stewardship' of the National Mall, the National Park Service, could take Scrotus to civil court for 'damages and destruction' and 'illegal use' of federal property. They also could swoop in with Law Enforcement Rangers to order everyone to disperse and shut it down. The LERs could arrest the 'organizers' (ie Scrotus) for illegal use of federal property, trespass and I suppose a host of other violations. I've seen Rangers break up a few illegal 'events' before and they're very good at it!
But do we really see that happening? Secty of Interior Doug Burgum is so far up Trump's arse he could extract his wisdom teeth with a torch. Burgum is why we have the destruction of the beautiful WH lawn for Scrotus' UFC fiasco and the painting of the reflecting pool. Not to mention all the orders that are resulting in the destruction of our nationally held lands.
Then you run up against the 'in performance of his duties' bullshit which is exactly what he'd say he was doing AND the fact that although he'll say 'he' is doing something there is actually layer upon layer of 'others' that are actually and legally in the line of fire. This is another thing he's great at. Creating a legal 'buffer zone' of minions between him and wrongdoing.
Theoretically, what would end up in court would be lawsuits filed by third parties 'with a vested interest' in protecting and preserving our public lands, like the National Parks Foundation, the Sierra Club, and the Public Lands Foundation to name a few.