Earlier quoted context omitted.
deconvolution, but it's more art than science because the problem is ill conditioned and blows up without regularization-- particularly if any part of the spike is overexposed (which it usually as you only notice the spikes on extremely bright stars).
Hmm - maybe a use case for (trained?) machine learning? I don't have much idea about ML so not sure if it makes any sense.
There is machine learning to remove stars called starnet, though last I checked it doesn't to an great job with diffraction that severe. Starnet is used by astrophotographers to enhance the contrast of nebula without getting artifacts from stars or to make completely starless nebula images.
If someone got starnet to remove the stars in the JWT images it wouldn't then be hard to go overlay stars back in without the diffraction.