Pull the staple, use a thin superglue to patch the tire, then if you really want to, put a boot inside the tire (e.g. cut a circle out of a dollar bill and superglue it to the inside of the tire.
Then ride that tire and don’t worry… the patched part of the tire will probably be the strongest and most puncture-resistant part of the tire.
I am going to assume you are running latex tubes. The first thing is to pull the staple, mark the side of the tire with something like a Sharpie, and put a glue-less patch on the inside. Inflate the tire and look for a bulge on the sidewall where the staple went in (the Sharpie mark). No bulge means no loss of structural integrity of the casing. If this is the case , add some fresh sealant to the tube and inflate to your normal pressure and go racing. As long as butyl tubes hold air you should be fine, but slow.
If you notice a bulge in the casing, go to Excel Sports in Boulder for some new 5000s. They are a faster tire and more flat resistant and have a lower rolling resistance than your 4000s,
Oh hell no, its not worth the chance, not to mention piece of mind. Maybe for indoor training, but I’d never use that tire outdoors again, especially risk it in a race. This coming from someone who has tried to cheap out, and has crashed with a blow out. A small nail, tack or thorn is one thing, but that staple is not only thick, and caused a two hole puncture, but it also looks ripped between the holes. That’s just asking for trouble. I’ve had the same thing happen when I picked up a fish hook. New tire, and no one gets hurt.
In my world view, if you have to ask if a tire needs to be replaced, it does. I would just ditch it. The cost of a new GP4K2 is around $30. That is only four lattes. And, the hassle of a flat is huge. Why ride with uncertainty when there is a cheap solution.