Brandon,
I will try your suggestion later. But - in what I got into trouble for calling a foolish procedure - Framework sent me a whole stack of untested ‘input covers’ and they all had the problem, even before I fitted them to the laptop. So I think that at least a whole load of the keyboards have the problem.
Pressing the problematic key in the manner that you suggest does indeed remove - at least sometimes - the scratching sound. I think that your diagnosis is correct and I seem to recall someone else making the same diagnosis. But not every Framework keyboard has the problem and not even, I think, every instance of the F13 keyboard (not even from one and the same generation).