I've found a .png file that has the "pinned" icon on it - but the color is red, not grey.
It is in MATLAB\R2019b\toolbox\simbio\web\analysisapp\release\simbio\images
The filename is ind_pinned.gif. Changing it does not change the icon used on the model graphics.
After a bit more searching I'm coming to the conclusion that the icon is hard-coded into the program. Can MathWorks confirm?
The current icon is pretty obtrusive. At a minimum I'd like to be able to turn those pinned icons off.