Re: Remington UMC model 51
Simpson's Ltd. has a worn but un-pitted Model 51 in 380 for $495. They usually ask top dollar for whatever they have, so yours is probably worth...considerably less, as Jim K suggests.
The problem with guns in that shape can be finding a buyer at any price. I bought a 51 in worse cosmetic shape than yours in order to practice dismantling it; I had a minty one I did not want to mess up. I paid $175 for it, and sold it for about $150, IIRC. It was a 32 ACP.