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Abstract: Fractional quantum Hall (FQH) edges with proximity-induced superconductivity can host parafermionic zero modes (PZMs), making them a promising platform for topological quantum computing. Recent experiments [Gül et al., Phys. Rev. X 12, 021057 (2022)] measured the edge conductance from crossed Andreev reflection (CAR) between counter-propagating FQH edges separated by a narrow superconductor. The observed conductance was small and non-quantized, with two distinct behaviors: some states show temperature-independent conductance, while others show conductance that grows as temperature decreases. We explain these results by dissipation to sub-gap modes in the superconductor and present a phase diagram for the FQH-superconductor junction. We show that for Jain states, temperature-independent non-quantized conductance occurs only in the presence of an integer mode (such as at filling $ν=1\pm\frac{1}{m}$, with odd $m\geq3$) strongly coupled to the dissipative channel. The predicted temperature trends qualitatively agree with the experiment, which shows temperature-independent conductance for $ν=2/3$ and integer states, but not for $ν=1/3$ and $ν=2/5$. We propose comparing $ν=4/3$ and $2/3$ to test the predicted influence of the relative chirality of integer and fractional modes.