I wonder--would this qualify as a thriller or a romantic thriller? Where is the emphasis? A nice mix between thriller and romance might work. This might turn into another 'tough guy' beats his way through government agents type of book.
This story is very similar in concept to The Humans by Matt Haig, in which an alien is sent to earth to kill a mathematician who'd unlocked the secrets to the Riemann Hypothesis, which would lead to space travel.