Before revision:  Concretely, our algorithm takes input an \epsilon-corrupted sample from a k-GMM and (k/\eta)} time, } outputs an approximate clustering that misclassifies at most O(k\epsilon)(\epsilon} +\eta  fraction of the points whenever every pair of components is separated by 1-\exp(- poly (k/\eta)  ) in total variation distance.
After revision:  Concretely, our algorithm takes input an \epsilon-corrupted sample from a k-GMM and whp in d^{\text{poly(k/\eta)} time, } outputs an approximate clustering that misclassifies at most O(k\epsilon)(\epsilon} +\eta fraction of the points whenever every pair of components is separated by 1-\exp(- poly (k/\eta) ) in total variation distance.