  We make use of link Floer homology to study cobordisms between links embedded
in 4-dimensional ribbon homology cobordisms. Combining results of
Daemi--Lidman--Vela-Vick--Wong and Zemke, we show that ribbon homology
concordances induce split injections on $\mathcal{HFL}^-$. We also make use of
the torsion submodule of $\text{HFL}^-$ to give restrictions on the number of
critical points in ribbon homology concordances.
