Put the squeeze on Mexico, depriving the Left of propaganda photo-ops. If they were motivated, they could end this quickly, and do so non-violently. They could halt and impound the buses that are transporting these thousands of people. They could arrest the caravan leaders, then arrest those who stand to replace them. Repeat as necessary. Then reroute the no-longer-organized followers southward.
Take out the buses and the food supply and they will run back home.