Well, if I had been asked to review a proposal to do this work, I almost certainly would have given it a poor review. If I had been on the NASA proposal review panel reviewing proposals and reviews (a task I have done in the past, and might do again in the future), and the proposal pile included this one, I almost certainly would have voted against it.
However, that was (hypothetically) then. This is (actually) now. As an experimentalist, with two (the Chinese, and this NASA) sensible looking papers claiming "anomalous" results, it can't just be ignored and it has to be looked into. And, this is cheap science - it won't take a LHC to disprove it. I don't have a University Lab, but, if I did, and if it was suitable, I would be thinking of getting physics undergraduates to do this test next term - which would be a good teaching opportunity, even if the ideas turn out to be BS.
Now, if you want to talk about the enormous opportunity cost from string theory, I would have a lot to say, but not in this thread.