Simple solution: build the wall such that their plot of land is on the Mexican side. Done.
Why bother with ceding the land? We could easily turn this into a positive. Build the wall around the property, open on the Mexican side, and dump all the people who don't like their own country into the void.
There are any number of college profs and other libs, like Hanoi Jane, and the staff of MSNBC, who could appreciate a truly lawless patch to call their own...
I wonder if the property has water?