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The discovery of the first two interstellar objects implies that, on average, every star contributes a substantial amount of material to the galactic population by ejecting such bodies from the host system. Since scattering is a chaotic process, a comparable amount of material should be injected into the inner regions of each system that ejects comets. For comets that are transported inwards and interact with planets, this Letter estimates the fraction of material that is accreted or outward-scattered as a function of planetary masses and orbital parameters. These calculations indicate that planets with escape velocities smaller than their current day orbital velocities will efficiently accrete comets. We estimate the accretion efficiency for members of the current census of extrasolar planets, and find that planetary populations including but not limited to hot and warm Jupiters, sub-Neptunes and super-Earths can efficiently capture incoming comets. This cometary enrichment may have important ramifications for post-formation atmospheric composition and chemistry. As a result, future detections and compositional measurements of interstellar comets will provide direct measurements of material that potentially enriched a sub-population of the extrasolar planets. Finally, we estimate the efficiency of this enrichment mechanism for extrasolar planets that will be observed with the $\textit{James Webb Space Telescope}$ (JWST). With JWST currently operational and these observations imminently forthcoming, it is of critical importance to investigate how enrichment from interstellar comet analogues may affect the interpretations of exoplanet atmospheric compositions.