You are correct. You can't remove from within Trimmer.
You "Trim" in Trimmer.
Meaning, I can scrub a selection Trimming-UPTO the beginning of the outtake - call this A - and drag that portion A to the timeline. Then move to the other-side of the outtake, where I can scrub a selection Trimming-AWAY FROM the end of the outtake - call this B - and drag this remaining portion of the Clip to the Main Timeline.
I scrub what I want and drag this Trimmed portion to Timeline.
Now, there are some nifty To- and From-cursor icons to do this and also the key-presses. I find it far more satisfying to do the method I outlined. It is faster and I find gets me into a real rhythm.