I would be very leery about removing the patch. Not because it is hard but kind of because there are some unknowns. If you want to remove the patch, you can use a seam ripper or a pair of very pointy scissors, and kind of snip at the threads holding it on being careful not to snip into the jacket. Here are the possible issues, the thread holes might not go away, then you'd be stuck with a bunch of holes where the patch was. You could check for that by testing the material with a needle in a hidden place and washing ideally would take care of any holes. Another possible scenario is that the patch is also "ironed on" which could be obvious once removed. And finally, there may be some sort of mark on the fabric to show where it is supposed to go. I removed some embrodiery from a skirt for the youngest once and underneath was permenant blue ink in the shape of the original design. That is much less likely though.
What I would do is this. I'd check and see if the fabric is likely to show the holes. If that is good, I'd try and see if I could "separate" the patch from the fabric underneath or snip a few stitches and check. And if all that works out, I'd take the patch off and hope for the best.
Veronica
Miss Ellie 11/03
Baby Audrey 4/08