Personally I would try to find out from Trek if that cup is bonded into the frame and if so, removal would be a no no. It does appear to have a concave surface designed to be in direct contact with the bearing balls and not a drop in cartridge bearing which is why I suspect that it's part of a cartridge that's come apart and stuck to an integrated bearing headtube cup but I'm not certain, so you need to find out for sure before trying to remove the rusted cup. Your photos show that there are two orange seals (photo #2 and one of them is covered in rusty gunk) that look like seals from a cartridge bearing like the one seen in your photo of the top headset bearing. If you can determine that the rusty cup in the headtube can be removed, soak it in PB Blaser or similar to make it easier to remove without using heavy duty methods.