If you don't want to plug the USB cable directly into the Teensy, which is located on the underside of the PCB under the spacebar, then yes, you need that part. You need to solder four wires to it (don't know why they call it surface mount), and solder those into four holes with solder pads in that vicinity on the PCB. Traces run from there to the solder points for the through hole USB receptacle on the rear edge of the PCB.
None of the switches have traces for LED backlighting, except for the "caps lock" switch location. The holes next to the LED holes have the traces for the indicator LED, so if you want a Caps Lock indicator, you need to bridge the LED solder points to the adjacent pads.
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Thanks for clearing the USB part up; just ordered those connectors. I'm still confused about the thing near the caps lock key, specifically this
component. What is it, do I need it, and where can I buy it?