You can use clear contact paper. There is a stained glass and mosaics forum on this site.

I'm presuming that the shiny metal is stainless steel, or has a finish that won't be damaged by solvents. It's hard to know what to suggest, other than trying a scrubbing pad and cleanser, or possibly a solvent like lacquer thinner, naptha, or MEK. If it were me, I'd call the manufacturer and get their advice as they will know what the metal is and what the plastic is. I also expect that you may be able to destroy/vaporize/carbonize the plastic just by using the grill on high.

We recently remodeled our master bath and installed new shower floor tiles. Its been about a month of using it and I start seeing a white deposit in multiple places in the shower tiles. No amount of cleaning is removing it. What could this be? Attaching photo for reference.

Maybe static electricity holding the dust. Give it a few weeks please.