We report on a high-pressure Raman study on two members of the La$_{1-x}$Ca$_x$MnO$_{3-delta}$ manganite family ($x=0.20$, $delta=0$ and $delta=0.08$). The results obtained for the $delta=0$ sample show a different behavior in the low and high pressure regimes ascribed to the onset of a new pressure-activated interaction previously invoked in other manganite compounds. The comparison of our results with literature data gives further support to the identification of the Jahn-Teller active stretching mode and shows that pressure-induced octahedral symmetrization is more effective in systems exhibiting a lower metallic character. On the contrary the new interaction sets in at pressure which decreases on increasing the metallic character of the system indicating a relevant role of the Mn-Mn hopping integral in its activation.