It’s just a prop to them. Why wouldn’t you take it home? I know why they wouldn’t.
They’d be better off waving fake fetuses around with “My Choice” on them. That would be something they’d put on their mantle. (Real fetuses would be thrown in the trash, of course, just like the flag.)
Heck I don’t even throw away the cheap towels I get handed when I go to some football games.