Those screens are really just thin glass sandwiches.

And they’re sharp too. When replacing a TV backlight I didn’t think about using gloves when lifting the panel. Welp, it can cut the skin a bit. If it slipped as I held it, that would have been fun for sure…
Anyway, the correct course of action is probably suction cups. Especially with larger panels. And a second person too. This was just a 32 inch panel.