The original argument (as I recall it from my youth) is that, since the fly must come to a stop before it reverses direction, then the train, too, must come to a stop.
Obviously the train doesn't stop, but nor does it slow down.
Only a molecule of two of the steel on the front of the engine would be affected, causing a miniscule denting, probably too small ever to be measured. If anything stops, it's only these couple of molecules. The compression of the steel would create a tiny amount of heat that would dissipate immediately, and, given the elasticity of the steel, the dent would bounce back to to form near enough the shape of the original smooth surface.
That's how I worked it out, all those years ago.