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±1/m, with odd m≥3) 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.