Not sure what's going on with your plant, but I would wipe it down well with a cotton ball damp with rubbing alcohol before considering giving up.

I think you have two problems. The drying is caused by dry/hot air. You need to increase air humidity around your plant. Best way is to stand the pot onto a tray filled with pebbles and water.
I am not sure about the infestation, wiping the leaves should help.
Your plant is definitely not a goner, I found this type of Calathea very sensitive to humidity. Just cut back the dry leaves.

Based on my own experiences with Calathea in California, I just wouldn't even bother.

They're so finicky and after all the work you'll put into recuperating this one, it'll be cloudy, or a friend will get pregnant, or it's hailing in Arkansas, and BAM -- it's ailing again.

While I might take that torture for gardenias -- I don't bother with Calathea anymore for that reason. It's probably the only plant I actually cussed at by myself. LOL

LOL, Sugi!