The arrow on the pistons in 2 stroke engines almost always point to the exhaust side (the only exception I know of is on the Fugi engines used in Polaris snowmobiles and ATV's where the arrow points to the mag side). I'd feel very confident that if your engine has run 200 miles already, the piston must be installed properly. Depending on the engine type, they will either fail very early with an improperly installed piston....or on some engines (this comes from my experience with some vintage snowmobiles) they will run for a long time, but perform terribly. I haven't tried running a backward piston in these mills to see what would happen, but my guess is.....a ring would likely snag an exhaust port within the first few minutes....and then the piston and cylinder would pack it in for good.
For anyone removing a piston, be very careful with the c-clips. They are real tiny and tricky to work with....be sure you do the work in a super clean area because the c-clips can go flying across the shop floor when removing them or installing them.....and finding a c-clip on a messy cluttered floor is a real pain (I searched over an hour for one the other day). Technically, you should never reuse a c-clip (even if the engine has never been run). But I took a chance and reused mine as I did not have any new ones and mine did not appear damaged. Also, when installing a c-clip in a piston, it should be installed with the gap facing either the top or the bottom....never have the c-clip gap on either of the sides. Reason being, if the gap is on the side, the constant up and down motion of the piston can eventually cause the c-clip gap to become compressed which will reduce the diameter of the clip and allow it to dislodge itself from the groove in the piston.