which parts of the engine transfer the thrust reaction force to the engine mountings and thence to the airframe?
As PBL said the spinny bits of the compressor are 'pushing' air backwards and according to newtons third law, the compressor blades want to go forward. It's then a case of the knee bone is connected to the shin bone.
Compressor(or fan/prop) blade pushes air back, blade goes forward, blade connected to disc(hub), disc connected to shaft, shaft connected to 'thrust' bearing, thrust bearing to bearing support, bearing support to engine case, engine case to engine mount, mount to aircraft, aircraft therefore goes forward.
Simple ... but the things that get pushed are not all in the forward direction and that's why most folks only talk about the exhaust when in fact it's the summation of the forward and the aft pushies
Exactly, compressors provide 'forward thrust' , turbines provide 'negative thrust' ie they are 'pulling back', exhaust cones provide forward thrust due to convergent duct. (let's not start on re-heat) As lomapaseo says, the 'sum' of these forces is the "thrust" of the engine.