The machined part acts as a pusher that pushes the bushing into the coupler. Its outside diameter is the same (or a little less) as the bushing because it pushes against the bushings outer metal sleeve and has to enter into the bushing bracket to completely push the bushing out. So since you bought a coupler into which the bushing fits, the machined part being about the same diameter should also slide into the coupler.

Note however that the bushing you are removing may be a bit larger in diameter and so may jam in the coupler. So it may be a good idea to file down the threads in the coupler on the side that will be accepting the bushing. When I pulled my TABs they stuck, but I couldn't be bothered setting up a rig to rotate the coupler while I filed the inside threads. Removal ie. bolt/nut turning was therefore a lot harder and when removed I had to knock the bushing out of the coupler using the machined part inserted from the other end with a hammer.
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1980 245 Canadian B21A with SU carb and M46 trans