How to cut already installed fiberglass insulation to add new recessed lights
If the basement is conditioned space, and what's above is conditioned space, the insulation is not doing much other than some possible sound reduction. (though if you don't cover it with drywall the paper may well play the role of fire hazard...)

If the fixtures ARE IC (insulation contact) rated, you can cut a hole that just fits. If they are NOT IC rated,you need to cut  considerably larger hole in the insulation and remove it, not "backfill" it. You can also do that just to simplify your life if there's no significant temperature difference between the basement and the space above it.