Auto detailing/cleaning clay has worked for me over the years. You have to try it in a small section and see how it works. That's always my first try. Then there are more serious products, more potentially damaging, if that doesn't work.
My experience with paint overspray has been a trial and error experience. You have to try clay and see. A lot depends on the base paint, it's condition, how long the overspray has been on the paint, what type of overspray, etc.. Normally, cleaning clay is a good place to start, then you can move to more robust type cleaners. I always try to start with the mildest product first and go from there.
Simple Green and a course cloth has worked for me in the Past as a "rougher".. followed up with a course automotive Rubbing compound (like Mothers) and a rag, then topped off with a good cleaner wax., and after its all done add some lindseed oil for a finish and it will look Great...do not use a tool with a cord on this or you will "burn" through the original paint, and watch where you leave the lindseed oil rag as it can self combust..
Damn, it's hard to stay out of these threads. LOL.
In being as diplomatic as I can:
Lye is a base, caustic and removes paint. Same as paint stripper. Use it on pin stripes that were laid down over automotive grade paints all you want. The lye eats the pin stripe first, because the pin stripe paint is an enamel, air cured. The lye will eat it first, because the underlying paint on a car that was painted after about 1975 is catalyzed. And of those, almost all of them now feature a top layer of urethane, also catalyzed. Oven cleaner, (lye) WILL eventually eat those too.
Still talking pin stripes, apply with a Q-tip. Buff car when finished with 3M Machine Glaze compound at 1500 RPM with a foam pad. This technique and oven cleaner, have nothing to do with over spray, and if you use it on a mini bike that was painted with rattle can- a highly touted method on here- you "will" eat into your paint.
Other polishing compounds will actually work, and depending upon their grit, may, or may not leave a cloudy (scratched) finish on the paint you're trying to preserve. I refer to metal polishes.
A clay bar is where I would start, good call for those who mentioned that. It depends on the level of over spray, and what the original paint is, and what the over spray is, and how long it cured in the air before landing on the paint. (any paint professional would have started with asking that question, because the answer is dependent upon it.)
Next choice would be the machine glaze I referred to above. It isn't cheap, and I use it with a Makita buffer- yes, it has a cord, and it a professional grade machine made for this purpose. It is variable speed, and it does not burn through. It is designed to "color sand" a paint job once the final clear coat is applied.
In the case of a mini bike with unknown paint, I'd apply the glaze with a soft, wet rag. If it didn't work, I'd switch to a cutting compound, also made by 3M, but there are other suppliers. Some of you will recognize it as more like the traditional "rubbing compound" you may have used. It is more abrasive than the machine glaze.
I have PM'd all of that and more to the OP, but since there is still interest in the thread, thought I'd clarify some comments, as well as add what someone with a few decades of experience does- as well as others in the business-Hope I don't sound like the usual OMB pontificating asshole here trying to compensate for my libido issues. I just know my way around paint. (and of course do tend to be an asshole)
Here is the Makita machine I use as well as the products I refer to.