There are several possibilities. You did not mention one: simply leave all as it is.
But it depends on the inner structure of your breeding tank whether this is a path to be followed. If it is well structured (by plants, wood, leaves or peat fibres on the bottom) and not put up only a few days ago I should change nothing. The backgroud is: if licorice gouramis find suitable conditions they will breed many times in short series. What you tell us could indicate that. Then probably young fish (not necessarily all) will survive (first in the bottom structures, later more below the surface). I needs time to find them (mostly about a fortnight). I you give some small portions of rotifiers or Paramecia or small Artemia they will find some food. The risk is that the old may take their young as food, but often this is not the case. The risk is low because they will breed next time within a few days (give good food as Culex or Moina or even fresh Artemia especially for the female). Then, at the second or third occasion – if you have seen them feeding on their larvae before – you could prefer a different method.
But this (leave the young with the parent-fish) surely works only if it is a well-structured tank. If it is a rather “naked” tank then you should catch the young out.
At any rate you should wait until the young are blackish and swim short distances within the cave. Then you could take a small tube and suck the content in a small tank. If your breeding tank is big enough you could place the small tank in it. A good method is to take a round glass of about two liters, placed separately, stir the water once a day, suck the debris from the middle of the bottom and replace with fresh water.
I should not catch the parents out of the breeding tank, for the reasons you described yourself.
But note: If you try to raise the young separately, you have to put full attention on feeding and hygienic conditions. This is much easier if you try raising some young within the breeding tank. Probably, you will loose some fry by this “natural” method, but for a beginner it’s easier. And with a later clutch you can use a different method, if necessary or in order to learn.