I got a couple annoying little marks on the glass of my PicoCalc from presumably some tiny grit that got into contact with it somewhere. Even though they were at the very edge of the screen and had no impact on the functioning of my PicoCalc, they were visible when light reflected off the glass, which persistently bugged me.
As a result I ordered new glass from Alex. He graciously only charged me the shipping, which was $8 USD, as he said the glass itself was very inexpensive. It took a total of 19 days from when I first sent him an email requesting to buy new glass to when the glass arrived, which was today.
To remove my old glass, because I had taped down my screen and did not want to untape it, I had to be creative. The strategy I ended up taking was to go to my local hardware store and buy a strong (5 lb load) suction cup. The suction cup ended up costing about $5 USD (it was actually part of a two-pack ─ I could not buy a single suction cup).
To actually remove the glass, I set down my PicoCalc on a surface with the screen facing up, and applied the suction cup to the old glass until it was completely stuck on. Then, I carefully but with a good amount of force pulled the suction cup away from the PicoCalc at an angle such that I pulled perpendicular to one of the edges of the PicoCalc. At first the glass stayed stuck onto the PicoCalc and required additional force before it came loose. The glass came off in one piece and neither my PicoCalc nor the glass were damaged in the process.
Once that was done I carefully removed the new glass from its packaging and protective layers, making sure to only touch its edges. I then set the glass on top of the PicoCalc in the proper orientation and used part of the protective layers to push it down without touching it with my fingers.
Even though I did my best to not touch the glass, there was a bit of residue from something on its outer side, so once the glass was on the PicoCalc I wiped it down with a clean, soft cloth, making sure not to touch it with my fingers. After that was done, the screen was pristine and free of any blemishes.