The amount of non-Neanderthal admixture in a European population can be measured using simply by looking at them: how many non-Nordic features do they have? If they for generation after generation have a purely Nordic look, then we can assume that they have no admixture at all. If they look like Middle Easterners, we can assume that they have much admixture. If they look overwhelmingly Nordic, but have a few non-Nordic features, we can assume that they are overwhelmingly Nordic, but have some (almost no) admixture.
We don’t need the politicized “science” of genetics to understand this.
Finally, yes, today we don’t look exactly like the ancient Neanderthals did, but…. of course we don’t. We have changed with time, with changing climates, with agriculture, with civilization: with auto-domestication. We are still Neanderthals though, only modern ones. And yes, the Nordic looking modern Neanderthals have close to no or even no non-Neanderthal admixture.