Encyclopedia of American Silver Manufacturers Dorothy T. Rainwater...2004 Revision notes a Hallmark Silversmiths Inc in New York, New York as of at least 1917. The line drawing of the mark is plain compared to your underscored version, but I wouldn't be too surprised if they're not the same outfit. The company Rainwater idenitified merged with Hunt Silver Co Inc in 1954 to form Hunt-Hallmark Co.
Oh by the way, it is no doubt sterling silver as marked. A nice looking cup. If it were mine, it wouldn't warrant repair, but it's too nice to get rid of. Clean it really good with silver polish and a fair amount of elbow grease; you'll be surprised how well it shines up, I think.