what color smoke ?? white or blue
this may be overlooking the obvious but...as was already said white smoke is unburnt fuel. Did they run it down the road to get it up to operating temp? if they just throttled it while sitting in the shop it is not warmed up and white smoke while cold is not unusual. make sure it's warmed up before worrying about any smoke. run it down the road a few miles, get it up to op temp and see if the smoke clears. these 2 strokes don't like to run cold, almost as much as they don't like to run hot. IMHO & FWIW
I agree they did not do there diagnostics. A compression test would have indicated the problem. The bad news now is that new fuel injector might not be to new by the time you get home if those cracked rings are coming apart and exiting through the combustion chamber. If need to be, I have a brand new set of pistons and liners for 8v71 that I could let you have for 800.00 which is half price. A rebuild gasket set is 130.00 and main bearings 50.00 and rod bearings 50.00. All you need is someone that knows 2 stroke detroits to do the labor.309-453-0963
There is another way to check without taking the exhaust off. crank it up and get a pot holder check the manifolds beside the cylinder. for heat if you have a large deference in the temp.
go ahead and drive it.