Sorry I just re-read your post and saw you were only talking about Software Manager. I don't believe there is any way to change the icon size in that directly, as you say it is connected to the gnome icon theme. There is another package called mintinstall-icons and not sure if this is installed by default, so you could check if this is installed and whether it solves the problem by installing it if not.
[Edit] your original post and add [SOLVED] once your question is resolved.
“The people are my God” stressing the factor determining man’s destiny lies within man not in anything outside man, and thereby defining man as the dominator and remoulder of the world.