I think the front end of this thing looks very much like the front end of the other $21.50 Amondo Tech 1W 1xCR123 light; and the 1xCR123 light looks exactly like the Sharper Image 1W LED light which was on sale for $20 last Christmas.
If both of these guesses are true, there are some threads about various attempts to replace the optics on the Sharper Image light (generally not easy - the Sharper Image light has hard to remove optics). BTW, the Sharper Image light was very nice and matches the descriptions given here (excellent machining, nice beam).
The Sharper Image light had an NX05 like optic which was backed up by an angled, bare aluminum retaining ring which held the LED in place. The retaining ring sort of looked like a reflector, but I'm not sure it added much to the light going through the optic.
BTW, my optics theory is kind of rusty, but adding a reflector behind an optic to send more light out the front sounds good but is harder to do than one would think. The LED is a more or less point source which a lens can focus into whatever beam you want. The light from the reflector would in effect be from a second source (minus infinity if the reflector were perfectly focused on the LED) which the lens would naturally reflect into a different pattern, so you would get not one stronger beam but 2 beams, typically the original beam and a ring outside that beam.
I tried some experiments with reflectors in the tiny Emilion $5 light which has an optic and the only thing I ever got was rings. The Inova people deserve their patent for the X0x/T0x TIROS optical systems because that's actually quite a trick they pulled off.