Ah, that's just the smoothing of the image, which indeed should be
turned off or at least follow the same logic as Tiled does when deciding
whether to smooth the map in the map view.
Fortunately for you, it's easy to work around by unchecking "use current
zoom level" (or making sure your zoom level is 100% when saving) and
then scaling the image up in an image editor using nearest neighbor
instead of linear interpolation (if you need it at 300%, that is).
Regards,
Bjørn