In response to the original question...
I find that these "spider veins" are a natural byproduct of closely spaced stars. The star removal morphological operations are helpless to construct bridges between the centers of these stars as they become eroded.
So what I found to be a partial remedy, going a long way toward elimination, but not quite total avoidance, of spider vein growth, is to use a two-stage star reduction. Concentrate on the faintest and smallest star images first, erode them, then attack the next higher level of star images.
I select out the faintest star images by using MMT with layers 2 & 3 (scales 2 & 4) selected, all others disabled, against a Luminance gray scale image. Then perform a 3 element morphological closing, followed by a 3 element dilation, and finally a Histogram midrange stretch to saturate most of those resulting islands. This builds the mask to be laid over the image, and then normal star reduction is applied using an iterated morphological selection with a 5 element disk kernel.
This may be sufficient star removal, and you could stop there. But if you are intent on removing all but the very brightest stars, the second stage will do that.
The second stage attacks the remaining brighter stars by repeating the same exercise, but with the initial MMT filtering layers 4 & 5 (scales 8 & 16) selected, all others disabled. Everything else remains the same.
Doing this in two stages helps to eliminate the growth of spider veins, since we diminish the faintest member of closely spaced star groups. The second wave of star shrinkage now has less intensity in whatever bridge remains between closely spaced brighter stars.