Is the reflected light still quantised?

I was going to post about low energy bulbs giving out quantised light rather than a full black body spectrum like a filament bulb. The reason is because high energy electrons are fired through a gas in the bulb. The electrons hit the gas atoms. This provides energy to knock different electrons that are bound within the atoms. The bound electrons jump up energy levels and then de-excite, emitting photons of light but only at the frequencies permitted by the electron level jumps. So you get a spectrum with discrete frequencies. I took this photograph with a diffraction grating to illustrate this point. But looking at it, the coloured part is the light from the lampshade - reflected light. It is from a white surface so it is likely to be the same as the bulb, but might it not tend back towards a full spectrum? Need to think about this.