If they weren’t gravitationally bound, they would have left the Milky Way billions of years ago.

Also, “in the halo” doesn’t necessarily mean “far from the center of the galaxy”; it means “not orbiting in the disk”.[1] Some of these stars are closer to the galactic center than the Sun.

[1] And further away from the center of the galaxy than the bulge — but the bulge is much smaller than the orbit of the Sun.