The first post made me think that you may have been too close to the white thingy when you took the picture, or the engine was also white and very very clean -sort of like that white cow in a snow storm sort of thingy. But the mystery of the white thingy (which is certainly a ballast resister) is that with only one wire between it and the coil, there is no 'hot' feature where the full +12v is powering the coil while starting. If you are not having any trouble starting the engine when cold, I'd let it be. There's nothing 'wrong' about running a ballasted ignition, but TR3s predated the crazy anti-pollution methods attempted and generally use a coil rated at the full +12v, instead of the lower rated coil. If you want to remove the resister, be sure to also replace the coil with a 'right' one.
If you ever have an ignition failure and want to check to see if the resister has failed, you can simply short across it and see if ignition is restored. If you try to run any significant length of time with the resister shorted, and a 'ballasted' coil installed, the coil will fail. In other words, you can short it out for a test, but not for very long. If you are the curious type, you can start the car and measure the voltage at the input (white wire) and the output (wire to coil) and see how much the ballast is dropping the coil voltage. My guess is you'll see from 12v to 14v depending on engine RPM/generator/alternator output on the white wire, and about 9v on the coil side.