One of the greatest mysteries in exoplanet science is whether planets can form in other galaxies. Claims of planets orbiting stars of extragalactic origin have been made over the last decade but none have been confirmed by independent studies. With the Gaia Data Release 2 in 2018, stellar proper motions and parallaxes could be used to identify stars which have motions that suggest they may have extragalactic origins. In this study, 1,080 low-luminosity red giant stars observed by both Gaia and NASA’s TESS mission with properties suggestive of extragalactic origin were systematically searched for planet transits. A series of injection and recovery tests were run to understand how sensitive the TESS data was to recovering a simulated planet signal. This sensitivity analysis was performed as a function of orbital period and planet radii as well as deducing how a signal to noise ratio (SNR) affects the recovery rate. Although no planet transits were detected in this sample, it was found that a planet with an orbital period between 3.5 days and 10 days and a planet radii greater than that of Jupiter has a 60.2% +3.7%/-1.4% rate of recovery. We compare this analysis to the completeness of K2 low-luminosity red giant stars. Given the known rate of occurrence for Hot Jupiter types of planets around similar stars within our Galaxy, we predict that an increase in sample size of a factor of 3-5 should be sufficient to either detect an extragalactic planet or distinguish between the occurrence rates of planets around the Milky Way and intergalactic stars.