I’d cut that shit right out and deal with the absorbency and gravity deficiencies later. The worst that can happen is the wall will no longer absorb as much gravity from the air and floats away to space because it’s no longer properly anchored. You can fix that problem with wall anchors above the cut and some caulk on the cut end to keep the gravity from falling out of the 2x4. Kitty gonna love the door. Good luck.