Yes it is safe to remove. Make sure to take not of each spring clip holding the glass in place. They will all have to be engaged securely when you are done and reinstalling the glass, otherwise the heat from the combustion chamber will melt delicate components in the control cavity(usually below the combustion chamber, where the fire is supposed to be)

Also, use ONLY amonia-free glass cleaner. (The foaming kind works best.) Or else the glass will develope a foggy haze again very quickly. If you dont have the proper glass cleaner use two damp rags and a dry rag. Wipe the outside of the glass with the damp rag then wipe the inside face of the glass. Scrub gently and make sure its all moistened. Then after a few moments reapeat that with the second damp rag to pick up all the loosened grime. If needed use a brand new razor blade or utility knife blade to scrape off any baked on residue. May have to re-wipe with another clean damp cloth before throughly drying both sides with the final cloth.

Edit: i forgot to mention i install and service fireplaces for a living.