No matter the stats of a pet equip if you trade it between characters it becomes a clean version. I tested this several times to make sure it wasn't just a visual bug after trading. I did this a few times after buying 5 red ribbons in hoping to scroll for 14 speed on a character. I ended up using around 70 scrolls while testing this to see if there was any differences or exceptions to this. No matter how it is scrolled when you trade it between characters they become clean. This is pretty broken because if someone fails a scroll they can just trade it between characters and come up with another clean on instead of having to buy another one.
If you drop them on the ground and pick up with another character then the stats/upgrade stay the same. So you could keep trading them to get a perfect stat one then just drop them between chars. Indeed broken.
Good point. I never tried dropping them between characters. I was in the fm when scrolling. So I never thought of doing that.