Leave the backing on.
It's not substantial enough to do any damage, and will slowly fall apart on a tube that's in use.
If you insist on removing it, peel off from the middle after having split it by folding the patch in half, backing side outside. Some patches have perforations in the backing to make the split easy.
Advice on instant patches should be accompanied by a hint on what make of patch and what tyres and pressures you run. Something that works well on a 26x1.75 tube in a 26x1.75 tyre at 35 psi may be an abject failure on a 700x18-23 tube in a 700x25 tyre at 135 psi.
FWIW, if I end up using both my spare tubes, I use the Park instant patches (on 700x28@80psi). They hold well over the medium term, but will get leaky over a year or so, and subsequent punctures stretching and unstretching the tube. My punctured tubes go in a heap at home, for repair in a batch, so they all get relatively fresh glue that's not been hanging about in an opened tube for a year or three.