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The Transiting Exoplanet Survey Satellite (TESS) is performing a near all-skysurvey for planets that transit bright stars. In addition, its excellentphotometric precision enables asteroseismology of solar-type and red-giantstars, which exhibit convection-driven, solar-like oscillations. Simulationspredict that TESS will detect solar-like oscillations in nearly 100 starsalready known to host planets. In this paper, we present an asteroseismicanalysis of the known red-giant host stars HD 212771 and HD 203949, bothsystems having a long-period planet detected through radial velocities. Theseare the first detections of oscillations in previously known exoplanet-hoststars by TESS, further showcasing the mission's potential to conductasteroseismology of red-giant stars. We estimate the fundamental properties ofboth stars through a grid-based modeling approach that uses globalasteroseismic parameters as input. We discuss the evolutionary state of HD203949 in depth and note the large discrepancy between its asteroseismic mass($M_\ast = 1.23 \pm 0.15\,{\rm M}_\odot$ if on the red-giant branch or $M_\ast= 1.00 \pm 0.16\,{\rm M}_\odot$ if in the clump) and the mass quoted in thediscovery paper ($M_\ast = 2.1 \pm 0.1\,{\rm M}_\odot$), implying a change$>30\,\%$ in the planet's mass. Assuming HD 203949 to be in the clump, weinvestigate the planet's past orbital evolution and discuss how it could haveavoided engulfment at the tip of the red-giant branch. Finally, HD 212771 wasobserved by K2 during its Campaign 3, thus allowing for a preliminarycomparison of the asteroseismic performances of TESS and K2. We estimate theratio of the observed oscillation amplitudes for this star to be $A_{\rmmax}^{\rm TESS}/A_{\rm max}^{\rm K2} = 0.75 \pm 0.14$, consistent with theexpected ratio of $\sim0.85$ due to the redder bandpass of TESS.

TESS Asteroseismology of the known red-giant host stars HD 212771 and HD 203949