The interstellar medium is less dense outside of galaxies, but it's already very sparse and it doesn't do much. It makes no difference to a star system that might be outside of a galaxy.

A star would have to make a near pass with a black hole or a neutron star to be slingshot into relativistic speeds, which almost certainly would not happen to a single star in a galaxy collision, statistically speaking. A star does not need to travel nearly the speed of light to escape a galaxy, but stars also almost never escape anyway because galactic collisions are so rare and are one of the few events capable of doing it. More likely, a star that escapes a galaxy is somewhere in a tail of matter being pulled away slowly from its home galaxy via a collision like pictured in the post, in a small chunk that the galaxy's gravity never recaptures.