Use something flat, not sharp, and plastic, not metal. Use some rubbing alcohol to dissolve the adhesive if it's stuck on there well, don't try to force it out with leverage because you may puncture. Once you have it out, place it in a sealed container, preferably metal and drop it off at your nearest repair shop, if they take batteries.

>I have been told by locals that the women who make this rugs usually make them in their home and are paid “fair”.

They're probably paid fair by local wages (which I'm guessing isn't that much) but nowhere fair compared to the markups they sell the rugs for.