You've considered a capitalist solution, but have you considered

Restorative justice: the spider is a trespasser, but will likely not find enough prey to survive. Capture the spider and relocate it to a suitable habitat where it can thrive. Check on it occasionally to ensure it is doing well

Libertarian anarchism: leave it be. It will die, survive, or thrive on its own terms

Authoritarianism: tell the spider if it doesn't remove itself it will be arrested, start ordering it to get on the ground, fire 13 rounds at it, preferably missing all shots but hitting a nearby toddler. Institute martial law against the "foreign threat", citing the recent death of a toddler