Yes, this can be done, but how easily depends on how hard or not the stone is. Yours is claiming to be an Amehata 雨畑 stone and I don’t have any experience working on those, but I’ll share what I can.
Get a couple waterproof silicon carbide papers of different grits (I won’t be giving any numbers because standards can differ on your end) and a grinding block to wrap the paper around. The paper will last longer when you moisten it properly. Start with a medium grit and smooth out the entire surface until the pit is gone. If this seems to take forever then you either need a more robust abrasive or more patience. Then move towards the higher grits.
The final surface will probably feel slippery and not good to grind ink on. To finish off the job, you may want to use something like the mud block from Inkston, Universal Stone, or even kitchen scrub with calcium carbonate such as Cif Cream (see this Japanese hobbyist’s experiment). Here’s another Japanese article on «opening» the inkstone.