My bike is back, and I'm ... puzzled.

[kiwi girl]

When you said you had a little plastic stick with wings left over the first thing I thought of was a dropout spacer (which is put in the dropouts when transporting a bike with the wheel out so that the forks don't get mashed together). Since your bike was packed by a pro they might have put one in. However if it was put in properly it probably shouldn't have come out of its own accord

If thats what it is then it is good that you have it left over