The entire grey plastic tower and components can be snipped right off, I left the leads for the LED (D1) on for ease of attaching the laser diode module, but you can just as easily pop the leads through the holes left from the LED if you have a solder sucker.
I marked the polarity in case you don't know your Anodes from your Cathodes :)

+ is Red / Positive / Anode
- is Black / Negative / Cathode

Step 3  Step 5