We present observations of $^{13}$CO(1-0) in 17 Combined Array for Research in Millimeter Astronomy (CARMA) Atlas3D early-type galaxies (ETGs), obtained simultaneously with $^{12}$CO(1-0) observations. The $^{13}$CO in six ETGs is sufficiently bright to create images. In these 6 sources, we do not detect any significant radial gradient in the $^{13}$CO/$^{12}$CO ratio between the nucleus and the outlying molecular gas. Using the $^{12}$CO channel maps as 3D masks to stack the $^{13}$CO emission, we are able to detect 15/17 galaxies to $>3sigma$ (and 12/17 to at least 5$sigma$) significance in a spatially integrated manner. Overall, ETGs show a wide distribution of $^{13}$CO/$^{12}$CO ratios, but Virgo cluster and group galaxies preferentially show a $^{13}$CO/$^{12}$CO ratio about 2 times larger than field galaxies, although this could also be due to a mass dependence, or the CO spatial extent ($R_{rm CO}/R_{rm e}$). ETGs whose gas has a morphologically-settled appearance also show boosted $^{13}$CO/$^{12}$CO ratios. We hypothesize that this variation could be caused by (i) the extra enrichment of gas from molecular reprocessing occurring in low-mass stars (boosting the abundance of $^{13}$C to $^{12}$C in the absence of external gas accretion), (ii) much higher pressure being exerted on the midplane gas (by the intracluster medium) in the cluster environment than in isolated galaxies, or (iii) all but the densest molecular gas clumps being stripped as the galaxies fall into the cluster. Further observations of $^{13}$CO in dense environments, particularly of spirals, as well as studies of other isotopologues, should be able to distinguish between these hypotheses.
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