Won't spot it first thing the very next time she comes back into the house? Good luck with that. Even if I glued dowels in and finished them to match the wood, plus patched the wallboard and painted it, my wife would walk through the front door and ask what happened and where the round spots in the wood that weren't there before had come from. And that's while she's still standing on the door mat getting her galoshes off and has yet to actually enter the kitchen. And she's got terrible eyesight, though I don't think that's a factor. It's more like some kind of second sight regarding anything I've done that she doesn't approve of.
If you want a bullet trap that won't wear out, but don't need to recover the bullets for examination, a 3/16" steel plate will stop a surprisingly potent round if it is 5 times longer than the target opening is tall, angling up off the ground toward the shooter with its long side. That is, a 1×5 foot plate with one of the narrow ends resting on the dirt and angling up to 1 foot higher at the target hanger end, presents a steep enough angle into the steel to deflect rather than stop a bullet directly. Then you just need clay or relatively rock-free earth or a sand pit beneath it, and not to miss either below or to the sides of the 1 foot square.