Get a Blitz cloth for jewelry and polish it up. Available on Amazon as well as other places.

Thanks Linda...going through their myriad of products...I'll see if I can find one suitable for turquoise. :)

The turquoise doesn't need polishing....just the silver. Sure you can't help rubbing the turquoise, but it's not a liquid so won't dissolve the glue.
the Navajo silvermiths use windex on a soft cloth to polish their pieces, turquoise, coral sugalite and all.

I've been polishing a lot of silver jewelry lately, including Native American. I use Weiman Silver Wipes. I'm told it's a good idea to polish the surface of carved areas but allow the designs below to remain dark.

Pretty much the same as a blitz cloth....but with a different name.