OK, OK, so I UTTERLY FAILED at the history of the "W" mintmark. I don't collect modern coins. I STILL stand by my statement that that random mark on the quarter in the OP is NOT a W. Anyone wanna disagree with THAT?
It's irritating when another informs you of the facts. I HATE THAT!! I learned very early to preface "statements" with "I believe", "it's reported", "I've heard", etc. prior to believed "important statements" of correction. I have a wonderful intelligent female friend who hardly ever corrects, but when she does the usual preface is: "DO YOU THINK THAT?...." That's when I know I'm about to realize my error without receiving a correction. It's a wonderful feeling from a like-kind individual! I believe a proper response to receiving a valid correction is: "I didn't know that", which I'm repeating more frequently with "advanced age" onset. I think our imagination allows great latitude, and I don't know whether a W is present on that coin. JMHO