Removing marker pen artifacts from scanned microscope slide images
You could also try local contrast enhancement or similar. Fiji has a function called Enhance Local Contrast (CLAHE) which does this. Looks like high pass filtering works reasonably well for you though.

As for your second question. The Gaussian Blur wikipedia you mention refers to Low pass filter. For the low pass filter each pixel is average over the surrounding pixels, weighted by a Gaussian centred on the pixel. In your case you are doing a high pass filter. This can can be given by the original minus the low pass filter, which is probably the easiest way of thinking about it (IMO).