I know of no prohibition against doing this, but if it was me, I would destroy it rather than take any profit from a piece of jewelry that is commonly worn by Masons "to exemplify the feelings of universal brotherhood which Freemasonry both teaches and embraces across the world," as this site explains.
From what I could find, there is no indication that this jewelry is presented in rituals, or is provided by leadership. It is purchased solely at the discretion of the member.
One of the most popular examples would be the Freemason ring, such as the one shown, which is worn "as a symbol of their ongoing obligation of loyalty, their brotherhood and as a visual statement that they are a member of the oldest fraternity on Earth."
It might be just another signet ring, but it symbolizes initiation into an organization condemned by the Church and which is personally offensive to me.
However, that's just my opinion. There is no hard-fast rule (that I can find) against melting down this jewelry and putting it to another use. If you're looking for a great company that buys and sells rare metals, 3 years in a row #1 on Trustlink makes Advantage Gold the highest rated gold seller.